Dale Fort Blog Number 22

25 10 2013

HALLOWEEN SPECIAL

There has been a human presence on Dale Point for at least 3000 years.  The original defences date from the Bronze Age and the site was occupied and improved through The Iron Age.  A carbon date of 790 BCE was obtained from the defensive ditch, making this the earliest physically dated site in Pembrokeshire. The site was probably inhabited into the Roman period and beyond.  The Normans controlled the Dale Peninsula during their occupation of South Wales and left evidence in the forms of the local church and castle.

During the First English Civil War (1642) the Dale Peninsula was held by Royalists who were said to have a gun battery on Dale Point, together with lodgings for 50 men.

By 1852 Charles Louis Napoleon had dissolved the Second Republic (of France), launched the Second Empire and begun calling himself Napoleon III.  This alarmed the British Parliament to the extent that it embarked upon a massive programme of coastal fortifications to defend against what was felt to be the imminent threat of a French invasion.  The current Dale Fort was constructed during this period (begun 1853, finished 1856).  The fort was occupied initially by 62 army personnel and ancillary staff.

By 1881 the buildings were occupied by a caretaker and his family and used sporadically for training the local Coastal Defence Militia.

In the 1890s the fort saw a military experiment unique in Europe.  The Zalinski Pneumatic Dynamite Torpedo Gun was installed and tested.  This weapon used air pressure to propel dynamite packed shells at incoming ships.  It worked but was very complex and rendered obsolete by later developments in high explosives.

From the 1890s the buildings were lived in by the Owen-Evans family.  During World War I Mrs. Owen-Evans operated the place as a military hospital.  In 1922 Miss M A Bland purchased the edifice and shared it with several orphaned girls, servants, various animals and Colonel Lee-Roberts, whom she eventually married.

During World War II the complex was taken over by the Admiralty and became an important mine-watching and de-gaussing station with a staff compliment of 15-20.

Since 1947, the fortress has been utilised as a residential field centre belonging to The Field Studies Council.  It specializes in the environmental sciences but also runs a large variety of arts, literary and historical courses drawing on the expertise of permanent staff and using that of external tutors.

Given the long period of occupation it’s hardly surprising that there have been several reports of ghosts and presences.  Some of these give a distinct impression of having been invented for entertainment purposes but there is no denying that both members of staff and visitors have on occasion been genuinely disturbed.

Here are some of the stories related to  or experienced by me over the past 3 decades:

The Face in the Window

In March 1987 Dale Fort was privileged to have the assistance of its first ever placement student. DA came to work for one year as part of her sandwich degree course.  She proved to be a diligent,  able assistant to the Academic Staff and was a popular and trusted member of staff.

In those days I lived on the premises,  occupying a small room on the floor above her.  In October 1987 I was awoken in the middle of the night by a piercing scream followed by a pounding on my door.  She had been returning from the bathroom to her own room and happened to glance at the un-curtained window that opened onto the stairwell. There had manifested a hideously deformed male form which leered and seemed to pass through the glass to approach her.  She ran back up the stairs seeking human company (namely me).  Needless to say, a thorough search revealed nothing and she was eventually persuaded to return to bed.  For the rest of her time with us, she kept the light on and pinned a permanently closed curtain to the window.  The window is still there, the curtain has gone, the rooms are still occupied.

The Headless Chicken of Saint Cadoc

An extremely odd manifestation this one, possibly the only ghost chicken ever reported, occasionally seen running up and down the corridors of C Block. This building was completed in the 1970s on the roof of the old gunpowder magazine.  Maybe somebody once kept chickens on the roof?  There are no reports as to the location of the chicken’s head.  A possible explanation of this bizarre tale is that the phantom bird was in fact a mature black-headed gull that became trapped in the corridor. The white body was seen easily in the dim moonlit corridor but the black head was not, giving the appearance of a headless bird.  Psychic Investigators have suggested that the chicken was called Mona.

ID’s Phantom

On the night of the 5th of February 2002, ID, Senior Centre assistant and Boatman was doing night duty (Dale Fort security and safety systems ensure that help is available to our visitors at all times). This entailed him staying in an unused dormitory room in the main barrack block (A Block). Feeling the need to answer a call of nature, Ian rose at about 1.40am and made his way to the ablutions. As he entered the appropriate corridor he registered a drop in temperature. The hairs (and there are plenty of them) all over his body stood to attention and he experienced a profound sensation of unease. Glancing down the corridor he observed an eerie glowing light. The presence appeared to hover just above the ground. It made progress down the passage and disappeared through the door to the main entrance lobby. Ian informed us that he spent the rest of the night awake with the light on.

In 2004 a visitor who claimed to possess psychic powers experienced perturbations at roughly the same spot.

The Giant Bat of Saint Bride

This unearthly phenomenon terrified a group of 54 GCSE pupils and is interesting as an example of mass hysteria.  They would not enter the accommodation block; they would not even approach the entrance.

THERE WAS A GIANT BAT ON THE ROOF.

No there wasn’t, there was a dustbin liner wrapped around the chimney pot, flapping in the wind.

The Cavalier

In 1984  JL the Dale Fort Cook (who was celebrated for his prosaic outlook and lack of imagination) entered the dim passage behind the dining room to adjust the boiler controls for the kitchen hot-water supply.  Minutes later a shriek was heard and he was seen exiting said corridor faster than anyone had ever seen him move before.  He was found shaking with fear in his room with a half-empty emergency bottle of cooking sherry and this story.  He had just finished adjusting the emersion heater when he looked up and saw a luminous,  exotically dressed figure drifting towards him.  To his horror it seemed to be a Cavalier from the English Civil War.  Before he could move aside it had passed through him and out through the solid wall at the end of the passage.

At first glance this seems absurd.  The current Dale Fort was not built until 1856. However, it is known that during the English Civil Wars most of the villages along the Milford Haven shores including Dale were controlled by Royalists. Dale Castle was occupied by Royalist troops and according to John Barrett’s A Plain Man’s Guide to the Dale Peninsula there was a gun battery at Dale Point. Maybe a Royalist soldier still floats about the place in spectral form?

A later member of staff claimed to have seen a Vauxhall Cavalier estate car disappearing through the same wall. This seems to have been the product of a dimly recalled story coupled with over enthusiastic wine tasting.

Headless Bob of B-Block

Bob was a handy-man at Dale Fort. One of his tasks was to maintain the ablutions in B Block which in those days were extremely primitive. They blocked up very easily. There can be something good even about a situation as dismal as regularly blocked lavatories. In this case it was the joy afforded to the rest of the staff who had frequent opportunities to say things like: “Unblock the B Block bogs please Bob?” and other amusingly alliterative phrases.

One day, Bob was repairing a window in the said B Block and unwisely placed a sheet of plate-glass at the bottom of his ladder. He climbed the ladder to inspect the damage. As he reached the top he disturbed a bat ( most likely Pipistrellus pipistrellus) which flew out and caused him to slip from the ladder and fall on to the sheet of glass. Tragedy ensued because Bob’s head was severed and the force of the impact caused it to bounce into a nearby fire bucket. The ghost of Bob is said (by some) to wander aimlessly about the site of the old ablutions block carrying his head in the fire bucket demanding retribution from the bat (long since dead of course). Can this be even slightly true?

The Mysterious Tomato

Of all the reports of strange sightings at Dale Fort, surely this is the strangest. Not really a ghost, possibly a natural meteorological phenomenon as yet unexplained, maybe inexplicable.  Towards the end of the 1980s three people reported seeing a large red object resembling a tomato drifting about on Dale Point and emitting a bizarre barking sound at passing gannets.  Red spots before the eyes brought on by stress and overwork might be an explanation.

The Incident in the Dormitory

Finally, a recent account of disturbing events that took place in a dormitory  back in July 1962.  Last year I was teaching a large group of sixth form biologists at Dale Fort when their teacher remarked that her father had been a student at Dale Fort in his youth.  I am always on the look-out for interesting pictures or anecdotes from previous years and immediately showed an interest, thinking that there might be some material to add to my history of Dale Fort.  (Scattering Dreams, revised 2011, available from Dale Fort at a mere £5.00).

“That is unlikely” said my visiting staff member “given what happened…..”.

After some persuasion she related this strange tale.

Her father EB had been a pupil at a private school near Gisburn in Lancashire (then in Yorkshire).  The school had been visiting Dale Fort annually since 1955 to learn natural history and geography.  On their second day they had been investigating vernacular building styles and in the remains of an old stone cottage on the fort road had found some bones among the stones of a broken wall.  Their teacher thought they might have belonged to a wild-cat or other small predator.  They put the skull on the window sill in their dormitory.

The four boys occupying the dormitory went to bed rather early (school pupils were better behaved in those days) and were soon asleep.

At some point in the night EB awoke to hear a scratching sound that seemed to be coming from somewhere in the room.  There was a moon that night and the room was filled with pale light.  He could see the white of the skull gleaming on the window sill.

Suddenly the door banged open and a girl dressed in a long white night dress careered in to the centre of the room startling them all wide awake.  She was clearly deeply distressed and began screaming a more or less unintelligible diatribe that concerned someone called Janet (they thought) and a cat.  The boys were understandably a little perturbed by this and began to get out of bed to see if they could help.  Before any of them had managed to do this the girl turned and ran out, the door slamming shut behind her.

They all felt that this girl was in such distress that they should get up and do what they could to help.

EB was first out of bed and made for the door.  He turned the handle and failed to open it.

The door was locked from the inside.

spectral sillinessOxford University MSc Environmental Management students read this blog and were inspired to recreate the events described above.  Dale Fort Placement Student Joe Pitt took this unsettling photograph.

They unlocked the door and began a hesitant search but found nothing.  Everybody else in the block was asleep and all was quiet.  They returned to their room, relocked the door and tried to sleep themselves.  They must have eventually succeeded because they woke in the morning and noticed that the skull was gone.

In the 17th Century it was quite a common, if barbaric practice to imprison a small animal like a cat in a small chamber within the wall of a newly built house in order to deter evil spirits.

The 27th July 1962 was the 350th anniversary of the trial in York of Jennet Preston of Gisburne  accused of witchcraft.

My response to this was rational.  I felt sure that there were no locks on the dormitories until our recently fitted key pads.  Nonetheless I went to check out the relevant room and found that the doors were original and also that they had had their original mortise locks removed.

Most Dale Fort ghost stories are clear nonsense (see several examples above).  This one may also be nonsense but it’s one of the few that sent a genuine shiver up my spine.

In August 2006 the paranormal investigators The Ghost Investigation Team (GITs) spent the night in various parts of the buildings looking for phenomena.  Their findings are available at: www.ghostinvestigationteam.com

Don’t miss the next blog thrill-seekers

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Dale Fort Blog Number 21

24 10 2013

Welsh in 10 Minutes

Welsh is the oldest frequently spoken language in Europe.  In the early medieval period it was spoken all over northern Britain.  It’s used as a first language by about 20% of Welsh people.  Lots of people in Wales have knowledge of Welsh because it’s taught in nearly all primary schools and is a compulsory subject in nearly all secondary schools.  You will not become fluent after ten minutes of study but you might learn how to pronounce some words and some useful phrases.

  How to make the sounds:

 

Ll or ll   (two ls) is pronounced by putting your tongue loosely against the roof of your mouth and exhaling noisily while saying “l” (that is an English “l”).  Using this method you should find yourself able to say:  Llanelli  (A town in South Wales which has the highest number of urban Welsh speakers anywhere).

Dd or dd  (two ds) is pronounced as in the English hard “th” as in the.

So say: Prynhawn Dda (good afternoon)

Ch or ch Imagine you have a small crumb stuck in your throat, make the noise you’d make to clear the obstruction.  Use this method to say the word: Ty bach (= toilet/lavatory literally little house)

In Welsh the letter U is pronounced as a short I as in “pip.”

The letter F is pronounced as an English V.

The letter I is always a long I as in pipe.

Say your first phrases:

HELPU! Ble mae’r ty bach agosaf?  (= Help! Where is the nearest toilet?)

Ble mae y tafarn agosaf? (= where is the nearest pub?)

Ble mae fy nhrowsus?  (= that was quite a party.  Lit. Where are my trousers?)

Welsh place names usually have a clear meaning:

Aberdaugleddau (Milford Haven) = Mouth of the two Cleddaus

Aberystwyth = Mouth of the Ystwyth (a river)

Eglwyswrw = Wrw’s Church

Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch

St Mary’s Church (Llanfair)

in the hollow (pwll)

of the white hazel (gwyngyll)

near (goger) the rapid whirlpool (y chwyrndrobwll)

and the church of St Tysilio (llantysilio)

by the red cave (gogo goch)

More useful words and phrases:

Diolch = thankyou

Diolch yn fawr = thank you very much

Dim diolch = No thank you

Os gwellwch yn dda = Please

Ga’ i = Can I?

Bore da = Good day

Prynawn Dda = Good afternoon

Nos da   = Good night

Wi’n hoffi coffi  = I like coffee

Wi ddim yn hoffi coffi   = I don’t like coffee

Ga’ i pysgod a sglodion os gwellwch yn dda?   = Can I have fish and chips please?

Mae’n flyn da fi, wi ddim yn siarad Cymraeg, wi’n Saesneg a twp

= I’m sorry, I don’t speak Welsh, I am English and thick.

Cwpaned o de osgwellwch yn dda   = A cup of tea please

Cwpaned o de gyda llaeth ac swgr os gwellwch yn dda

= A cup of tea with milk and sugar please

Cwpaned o de heb llaeth a siwgr os gwellwch yn dda

= A cup of tea without milk and sugar please

Symud dy din     = You appear to be sitting on my beach towel

Ble mae esgidiau   = It was the fault of my underpants

Fy hofrenfad y llonaid o llyswenau  = My hovercraft is full of eels

Nadolig Llawen   = Merry Christmas

Penblwydd Hapus   =  Happy Birthday

Croeso i Gaer Dale    =  Welcome to Dale Fort

Ach a fi  = I find all this rather distasteful

Popty Ping  = Microwave oven

Yn dod a dealltwriaeth amgylcheddol i bawb

= Bringing environmental understanding to all

Wi’n hoffi moron=  I like carrots

Don’t miss Blog 22 which also will not be about statistics





Dale Fort Blogs 1-25 Contents

11 10 2013

Dale Fort Blog Contents

Number 1

All about nematodes

https://dalefort.wordpress.com/2012/03/

Number 2

3 You Tube clips:

Starlings at Mabesgate

Error Bars in Excel 2007

Measuring Heights on Seashores

https://dalefort.wordpress.com/2012/04/02/dale-fort-blog-number-2/

Number 3

The History of Dale Fort part 1 (all about the rocks)

https://dalefort.wordpress.com/2012/04/03/dale-fort-blog-number-3/

Number 4

The History of Dale Fort part 2  (the construction  materials of Dale Fort).  Far more exciting than it sounds, you won’t want to miss it, go there NOW

https://dalefort.wordpress.com/2012/04/18/dale-fort-blog-number-4/

Number 5

Sargassum muticum in Britain (with a video on how it makes babies)

https://dalefort.wordpress.com/2012/04/25/dale-fort-blog-number-5/

Number 6

The History of Dale Fort part 3, The First Humans

https://dalefort.wordpress.com/2012/04/

Number 7

Silverfish and their ways

https://dalefort.wordpress.com/2012/05/10/dale-fort-blog-number-7/

Number 8

The fat-bellied book chewer

https://dalefort.wordpress.com/2012/05/

Number 9

Seaweed research at Dale Fort

https://dalefort.wordpress.com/2012/07/

Number 10

Wormhole research at Dale Fort

https://dalefort.wordpress.com/2012/08/07/dale-fort-blog-number-10/

Number 11

Limpets and their mysterious ways

https://dalefort.wordpress.com/2012/08/27/dale-fort-blog-number-11/

Number 12

Anne, Bridget, Cadoc and David

https://dalefort.wordpress.com/2012/12/07/dale-fort-blog-number-12/

Number 13

St David and his friend Elvis

https://dalefort.wordpress.com/2012/12/10/dale-fort-blog-number-13/

Number 14

Dancing bananas:  Just how many are there?

https://dalefort.wordpress.com/2013/01/16/dale-fort-blog-number-14/

Number 15

Six-legged female vampires

https://dalefort.wordpress.com/2013/01/23/dale-fort-blog-number-15/

Number 16

Cry Havoc!  And let loose the dogs of accountancy………The History of Dale Fort part 6

https://dalefort.wordpress.com/2013/04/22/dale-fort-blog-number-16/

Number 17

Wee timorous beasties

https://dalefort.wordpress.com/2013/04/30/dale-fort-blog-number-17/

Number 18

A magical island where strange events take place

https://dalefort.wordpress.com/2013/07/02/dale-fort-blog-number-18/

 Number 19

The many faces of the mean (and by the way Bill, smoking is neither big nor clever)

https://dalefort.wordpress.com/2013/10/11/dale-fort-blog-number-19/

Number 20

Deviant Beards and other exciting topics

https://dalefort.wordpress.com/2013/10/11/dale-fort-blog-number-20/

Number 21

Welsh in 10 Minutes (ddim yn rhugl)

https://dalefort.wordpress.com/2013/10/24/dale-fort-blog-number-21/

Number 22

Halloween Special.  Read it with the light on……..

https://dalefort.wordpress.com/2013/10/25/dale-fort-blog-number-22/

Number 23

Back to matters more prosaic but useful I hope.  How to get a quick frequency distribution histogram out of Excel 2007

https://dalefort.wordpress.com/2013/11/06/dale-fort-blog-number-23/

Number 24

Spectacular weather, huge waves, the demise of a bridge, the scaring of a photographer and much more

https://dalefort.wordpress.com/2014/01/08/dale-fort-blog-number-24/

Number 25

BARNACLES so more than just the worst part of a keel-hauling

https://dalefort.wordpress.com/2014/01/10/dale-fort-blog-number-25/





Dale Fort Blog Number 20

11 10 2013

THE STANDARD DEVIATION

 of the mean is that they think that this attitude will bring them happiness.  It will not.

The standard deviation of a set of data is a measure of the spread of the data about the arithmetic mean value.  It represents the average amount that each value differs from the mean.

Alarm and despondency are spreading through the ranks of the RSPB (Royal Society for the Protection of Beards).  The trustees of the organization are deeply concerned that stubbly “designer beards” have been observed infecting the chins of some members.  These “shorty” appendages are strictly illegal, (minimum permissible length of 0.47m and willingness to house a homeless badger being the basic requirements for members).  You have been employed to investigate suspect groups and report back to the Minimum Standards (Pogonophilia) Committee.

You collect the following data:

Membership Category

Beard lengths in metres

Ecologists

0.1 0.9 0.4 0.5 0.5 0.5 0.5 0.6 0.5 0.5

Druids

0.4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6

Eco-Warriors

0.1 0.2 0.5 0.8 0.5 0.7 0.4 0.5 0.6 0.7

Plot out the data for each category of RSPB member as a line plot:

line plot of eco beard lengths finalAxis is in metres.  Mean Ecologist beard-length = 0.5m

druid beard length line plot finalAxis is in metres.  Mean Druid beard-length = 0.5m

ecpwarrior lineplot beard finalAxis is in metres.  Mean Eco-Warrior beard-length = 0.5m

  Notice that the arithmetic mean beard length of all groups is the same (0.5m).  The data for each group are however obviously different in the way that individual data points are scattered  about the mean.

 Nearly all Ecologists have beards of 0.5m (the mean value) but there are a couple of illegally short beards and two bigger growths (one you will note is of such massive proportions that it could conceal a veritable menagerie of nesting creatures).

  Druids are very consistent in their beard lengths.  Eight  out of ten measured growths are of 0.5m.  There is just one shorter beard (probably a trainee) and one slightly bigger version belonging to a non-conformist druid.

 The Eco-Warrior’s beard lengths are much more spread out around the mean, reflecting an inconsistant approach to bristle growth and (in 4 cases) blatent disregard for the constitution of the RSPB.

  How can we describe the differences in the 3 data sets?   What is needed is a measure that indicates the average amount that each piece of data is different from the mean.  The standard deviation is just such a number.

Here is how it’s calculated:

table of x - meanx = a piece of data      x-bar = the mean    sigma = the sum of

The first column (from the left) is each piece of raw data.

The second column from the left is the distance of each piece of raw data from the mean (i.e. Each piece of data minus the mean).

Note that if we just added this column up the values would cancel each other out and we end up with a value of zero.  Obviously this is no use as a measure of scatter of the data about the mean.

The way around this problem is to square each of the values from the second column.  The negative values now become positive values and we can add them up.  This has been done at the bottom of the third column (= 0.34).

So we now have a value (0.34) that represents the total deviation of all our Ecologists beard-lengths from the mean.  If we divided that value by the number of items of data we would have a measure of the mean amount that each bit of data varies from the mean.

There is a slight complication though.  If we could measure every single ecological beard in the world we could calculate the actual mean length of the whole population (μ).

Our sample however, has only ten measurements in it.  So to give us a more realistic estimate of the real mean we divide by one less than the number of samples.  In our case that = 10 – 1 = 9.  Statisticians call this value (n – 1) the degrees of freedom.  You almost  always use n – 1 to calculate standard deviation.

                                                                   0.34/9 = 0.037

We now have a number (0.037) representing the scatter or spread of our Ecologist’s beard lengths about the mean value.  Statisticians call this number the variance of the data and it is used in numerous ways that do not immediately concern us here.

Remember we squared all our differences from the mean to get rid of the negative values.  To complete our calculation of the standard deviation we must take the square root to convert the number back to its original units. 

√0.037 = 0.192  = standard deviation of Ecologist’s beard lengths in metres

The calculation we have just done can be represented by this formula:

SD

Now, think back to our original beard length data.  We needed a measure of the scatter of data points about the mean value.  We now have it: The standard deviation.  If we do the calculations for the Druids and the Eco-Warriors as well we get the following values:

Standard deviation (Ecologists)      = 0.192

Standard deviation (Druids)            = 0.047

Standard deviation (Eco-Warriors) = 0.221

Notice that the Druids (whose beards were all clustered around the mean) have a very small value.

The Ecologists (whose beards were mostly clustered around the mean but not to the same extent as the Druids) had a bigger value

The Eco-Warriors whose beard lengths were all over the place (i.e. widely scattered about the mean) have the biggest value of all.

Popular computer programmes (like Microsoft Excel for instance) will do all this and much more.  Scientific calculators will also save you the tedium of multiple calculations if you know how to operate their statistical functions.  Remember though that it might be a requirement that you show your working.

Look out for Blog 21…….. it won’t be about statistics.

 





Dale Fort Blog Number 19

11 10 2013

 POGONOPHILIA = Love of beards

POGONOPHOBIA = Fear of beards

NORMAL = Not feeling too strongly either way

Bill_Ballantine

In your work as Stubble Development Officer for the RSPB (Royal Society for the Protection of Beards), you are asked to determine just exactly how long are the member’s beards.

You decide to measure the length of beard of 11 randomly selected  RSPB members.

It’s taxing and itchy work and takes ages but eventually, you succeed.  Tired, but triumphant you present your data to The Grand Wizard Beard-Master of the RSPB.  “Hah!” she says.  “This is all very well, but I’m too busy to look at 11 numbers”.  “Can’t you give me one number that represents them all?”

YES you can.  You need a measure of the central tendency of the 11 beard lengths that comprise your data set.  You need to calculate an AVERAGE.

Averages

There are 3 kinds of average that concern us:

The arithmetic mean, the median and the mode.

THE ARITHMETIC MEAN

Most people will have heard of the arithmetic mean (commonly called simply the mean or in normal conversation the average)

If you add up all your beard lengths and divide by 11 you will have calculated the arithmetic mean of those 11 measurements:

Beard lengths/m:  0.2, 0.1, 0.5, 1.8, 0.1, 0.1, 0.2, 0.9, 0.2, 0.2, 0.6

0.2 + 0.1 + 0.5 + 1.8 + 0.1 + 0.1 + 0.2 + 0.9 + 0.2 + 0.2 + 0.6/11 = 0.45

= The arithmetic mean of your sample of 11 measurements.

The symbol for the arithmetic mean of your sample is: x bar

 This is an X with a line over the top (a bar) and so it’s referred to as X-bar.

Your X-bar is only based on 11 samples, it’s likely that if you measured more than 11 beards you would get a different result.  If you could somehow swing an invitation to the annual RSPB Awards Ceremony (which ALL members MUST attend on pain of shaving), you might measure the beard-length of every single member.

If you managed this unlikely feat, you would have the true mean of the whole population of RSPB beards.  This value is given the symbol: μ (mu, pronounced mew; the noise a cat makes).

For most things you might measure (e.g. Tree girths, shell-lengths, people-heights, seed-weights, nose lengths, IQs, whale-weights and so on) you will not be able to measure them all, so you will end up with sample arithmetic means.

Our value of x-bar (0.45m) is all very well, but did you notice that there was one measurement that was way different to the others?  Obviously that was the chin-wobblingly astonishing 1.8m example (fourth from the left in the list).  Including this observation makes our average much larger than it otherwise would have been.  This makes our arithmetic mean not very representative of the sample as a whole, which (if you remember back to the beginning) is sort of, the whole point.

DO NOT DESPAIR…… We can get around this catastrophic situation by using a different kind of average:

THE MEDIAN

To obtain the median all you do is put the data in order (from lowest to highest) and find the middle value.  So for our beard-length data:

0.1,  0.1,  0.1,  0.2,  0.2,                     0.2,                      0.2,  0.5,  0.6,  0.9,  1.8

……………………………………………Middle value

Our median is 0.2.  Most reasonable RSPB members would accept that as a more representative value for beard-length than the arithmetic mean.

Astute readers will have noticed that your author has cunningly used 11 pieces of data in order to avoid the problem of what to do if there is an even number of items of data, where you would have no middle value.  All you do in that case is take the mean of the value of the middle pair thus:

1,  2,  2,  2,                                  3,  4,                                    4,  4,  5,  6

………………………………The middle pair of values

The middle pair are 3 and 4, so the median  = 3 + 4/2 = 3.5

The alternative to both the arithmetic mean and the median is:

THE MODE

The mode is a measure of central tendency based on the numbers of observations.  In our beard-length example the data were as follows:

0.1,    0.1,    0.1,               0.2,    0.2,    0.2,    0.2,            0.5,    0.6,    0.9,    1.8,

Three values of 0.1          Four values of 0.2      Just one of each of the other values

It’s clear that the most common value was 0.2, there are four items of data which have that value, so the mode is 0.2.

How might we measure the spread of values about the mean?

Read all about it in Blog Number 20.

coming soon…… be the first on your block to read it, include your zip-code and $1 postage