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

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

3. 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

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

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

7. 11.14286 © Taylor & Francis 2014

8. 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

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

10. 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

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

13. 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

14. 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

15. Student # ScoreStudent #Score 1st 4 ‒ 11.14286 = ‒ 7.14286 12th 13 ‒ 11.14286 = 1.85714 2nd 5 ‒ 11.14286 = ‒ 6.14286 13th 13 ‒ 11.14286 = 1.85714 3rd 7 ‒ 11.14286 = ‒ 4.1426 14th 13 ‒ 11.14286 = 1.85714 4th 8 ‒ 11.14286 = ‒ 3.14286 15th 14 ‒ 11.14286 = 2.85714 5th 8 ‒ 11.14286 = ‒ 3.14286 16th 14 ‒ 11.14286 = 2.85714 6th 9 ‒ 11.14286 = ‒ 2.14286 17th 14 ‒ 11.14286 = 2.85714 7th 9 ‒ 11.14286 = ‒ 2.14286 18th 15 ‒ 11.14286 = 3.85714 8th 10 ‒ 11.14286 = ‒ 1.14286 19th 15 ‒ 11.14286 = 3.85714 9th 10 ‒ 11.14286 = ‒ 1.14286 20th 15 ‒ 11.14286 = 3.85714 10th 10 ‒ 11.14286 = ‒ 1.14286 21st 15 ‒ 11.14286 = 3.85714 11th13 – 11.14286 = 1.85714 © Taylor & Francis 2014

16. S# Score ‒ mean Score ‒ mean 2 S# Score ‒ mean Score ‒ mean 2 1 ‒ 7.14286 51.02041121.85714 3.44898 2 ‒ 6.14286 37.73469131.85714 3.44898 3 ‒ 4.1426 17.16327141.85714 3.44898 4 ‒ 3.14286 9.87755152.85714 8.16327 5 ‒ 3.14286 9.87755162.85714 8.16327 6 ‒ 2.14286 4.59184172.85714 8.16327 7 ‒ 2.14286 4.59184183.8571414.87755 8 ‒ 1.14286 1.30612193.8571414.87755 9 ‒ 1.14286 1.30612203.8571414.87755 10 ‒ 1.14286 1.30612213.8571414.87755 111.85714 3.44898Σ (score – mean ) 2 = 236.57144 © Taylor & Francis 2014

22.  Mean = 11.14286  Median = 13  Mode = 13 and 15  Range = 11 points  Standard deviation = 3.42927 © Taylor & Francis 2014