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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.


&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&iden,fying&the&value&at&the& midHpoint&(see&right).&In&this&case&the&midHpoint&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.&&


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


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


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?’


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