Using statistics in small-scale language education research Jean Turner © Taylor & Francis 2014

There are three measures of central tendency:  Mean  Median  Mode © Taylor & Francis 2014

The mean is the mathematical midpoint of a set of interval scores.* The formula is: * Or interval-like, continuous ordinal scale data © Taylor & Francis 2014

Student #ScoreStudent #Score 1st412th13 2nd513th13 3rd714th13 4th815th14 5th816th14 6th917th14 7th918th15 8th1019th15 9th1020th15 10th1021st15 11th13 © Taylor & Francis 2014

Student #ScoreStudent #Score 1st412th13 2nd513th13 3rd714th13 4th815th14 5th816th14 6th917th14 7th918th15 8th1019th15 9th1020th15 10th1021st15 11th13Σ = 234 © Taylor & Francis 2014

© Taylor & Francis 2014

The median is the score that’s located at the physical center of the set of scores.  When there’s an uneven number of scores, the one in the middle is the median.  When there’s an even number of scores, identify the two in the middle and find the mean of those two scores. © Taylor & Francis 2014

Student #ScoreStudent #Score 1st412th13 2nd513th13 3rd714th13 4th815th14 5th816th14 6th917th14 7th918th15 8th1019th15 9th1020th15 10th1021st15 11th13 Σ = 234 © Taylor & Francis 2014

The mode is the most frequently occurring score in the set of scores.  The bar plot in the next slide shows that the set of 21 scores has two modes, the scores of 13 and 15.  The set of scores is bimodal. © Taylor & Francis 2014

There are two measures of dispersion:  Range  Standard deviation © Taylor & Francis 2014

The range is the number of points between the lowest and the highest score in the set.  The lowest is 4 and the highest is 15.  15 – 4 = 11  The range is 11 points. © Taylor & Francis 2014

The standard deviation is the mean distance of the scores from the mean, expressed as a number of points. The formula is: © Taylor & Francis 2014

Student # ScoreStudent #Score 1st 4 ‒ = ‒ th 13 ‒ = nd 5 ‒ = ‒ th 13 ‒ = rd 7 ‒ = ‒ th 13 ‒ = th 8 ‒ = ‒ th 14 ‒ = th 8 ‒ = ‒ th 14 ‒ = th 9 ‒ = ‒ th 14 ‒ = th 9 ‒ = ‒ th 15 ‒ = th 10 ‒ = ‒ th 15 ‒ = th 10 ‒ = ‒ th 15 ‒ = th 10 ‒ = ‒ st 15 ‒ = th13 – = © Taylor & Francis 2014

S# Score ‒ mean Score ‒ mean 2 S# Score ‒ mean Score ‒ mean 2 1 ‒ ‒ ‒ ‒ ‒ ‒ ‒ ‒ ‒ ‒ Σ (score – mean ) 2 = © Taylor & Francis 2014

 Mean =  Median = 13  Mode = 13 and 15  Range = 11 points  Standard deviation = © Taylor & Francis 2014