measure&#38;of&#38;average.&#38;&#38;&#38;

In such circumstances as the above, a more reliable measure of average would be the Median value. This is obtained by rearranging the data into numerical order and then identifying the value at the mid-point (see right). In this case the mid-point value can be found between the 5th and 6th value when arranged in order. This is £10 and is clearly a more reliable measure of average for 9, out of 10, of these learners.

&#38;In&#38;such&#38;circumstances&#38;as&#38;the&#38;above,&#38;a&#38;more&#38;reliable&#38;measure&#38;of&#38;average&#38;would&#38;be&#38;the&#38;Median&#38;value.&#38;&#38; This&#38;is&#38;obtained&#38;by&#38;rearranging&#38;the&#38;data&#38;into&#38;numerical&#38;order&#38;and&#38;then&#38;iden,fying&#38;the&#38;value&#38;at&#38;the&#38; midHpoint&#38;(see&#38;right).&#38;In&#38;this&#38;case&#38;the&#38;midHpoint&#38;value&#38;can&#38;be&#38;found&#38;between&#38;the&#38;5th&#38;and&#38;6th&#38;value&#38; when&#38;arranged&#38;in&#38;order.&#38;This&#38;is&#38;£10&#38;and&#38;is&#38;clearly&#38;a&#38;more&#38;reliable&#38;measure&#38;of&#38;average&#38;for&#38;9,&#38;out&#38;of&#38;10,&#38; of&#38;these&#38;learners.&#38;&#38;

A summary of some common ways of describing quantitative data is shown below.

! A&#38;summary&#38;of&#38;some&#38;common&#38;ways&#38;of&#38;describing&#38;quan,ta,ve&#38;data&#38;is&#38;shown&#38;below.&#38;

Descriptive! Statistics

(Arithmetic) Mean – commonly known as the average = sum of values/number of values

Median – the middle value when all the values are arranged in order from lowest to highest

Mode – the most frequently occurring value (most appropriate when measuring the number of occurrences within a category e.g. eye colour)

Range = difference between the highest and smallest values

Interquartile Range – (a) arrange all the values in order from the lowest to the highest; (b) work out the values that lie at the ¼ and ¾ positions along the series (similar process to calculating the median, which is the value at the ½ way point) – these are the 1 between these two values – its purpose is to avoid extreme values giving a false impression of the spread of the data.

Note 1: measures of average (mean, median and mode) tell you where the bulk of the data lies - (if the average height of men is 5’7”, then most men are somewhere around this height). Note 2: measures of variance (range and interquartile range) tell you how far the data spreads around this average.

Drawing%conclusion%(from%knowledge%to%wisdom)% Drawing conclusions (from knowledge to wisdom)

You will need to draw conclusions from the knowledge you have gained from carrying out your project. This requires a thorough, critical evaluation of what your analysis of results truly indicate and whether these conclusions can be used as a reliable evidence-base for future action (e.g. to further ‘roll-out’ your intervention or to initiate further research). A central judgement to be made here will be to consider ‘can we be sure that there has been a real change/ improvement?’

You&#38;will&#38;need&#38;to&#38;draw&#38;conclusions&#38;from&#38;the&#38;knowledge&#38;you&#38;have&#38;gained&#38;from&#38;carrying&#38;out&#38;your&#38; project.&#38;&#38;This&#38;requires&#38;a&#38;thorough,&#38;cri,cal&#38;evalua,on&#38;of&#38;what&#38;your&#38;analysis&#38;of&#38;results&#38;truly&#38;indicate&#38; and&#38;whether&#38;these&#38;conclusions&#38;can&#38;be&#38;used&#38;as&#38;a&#38;reliable&#38;evidenceHbase&#38;for&#38;future&#38;ac,on&#38;(e.g.&#38;to&#38; further&#38;‘rollHout’&#38;your&#38;interven,on&#38;or&#38;to&#38;ini,ate&#38;further&#38; research).&#38;A&#38;central&#38;judgement&#38;to&#38;be&#38;made&#38;here&#38;will&#38;be&#38; to&#38;consider&#38;‘can&#38;we&#38;be&#38;sure&#38;that&#38;there&#38;has&#38;been&#38;a&#38;real&#38; change/improvement?’&#38;

Consider&#38;the&#38;‘before&#38;and&#38;a\er’&#38;results&#38;shown&#38;as&#38;two&#38; parallel&#38;barHcharts,&#38;to&#38;the&#38;le\.&#38;It&#38;is&#38;clear&#38;that&#38;there&#38;has&#38; been&#38;a&#38;shi\&#38;in&#38;the&#38;modal&#38;average&#38;from&#38;‘2’&#38;to&#38;’4’,&#38;but&#38;the&#38; range&#38;(variability)&#38;of&#38;the&#38;data&#38;is&#38;fairly&#38;‘wide’&#38;in&#38;both&#38; cases.&#38;&#38;Is&#38;this&#38;evidence&#38;of&#38;improvement&#38;or&#38;simply&#38;

39

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