By Douglas M. McIntosh (Auth.)
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Additional resources for Statistics for the Teacher
The following table gives the marks of eight pupils who were being sidered for scholarships on the basis of examinations in English mathematics; the mean mark and standard deviation of all pupils sat the examination were respectively ME = 40, σΕ = 10 (English), MM σ = 20 (mathematics). conand who = 50 COMPARISON AND A D D I T I O N OF MARKS Pupil A Β C D Ε F G H English Mathematics 60 30 42 50 20 45 40 30 70 30 80 84 65 65 50 70 57 Find (a) the order of merit of the eight candidates when the raw marks are added; (b) the order of the combined marks when the standard of marking and the scatter of marks are made to be the same as the English mark by calculation; and (c) the order of the combined marks when the standard of marking and the scatter of marks are made to be the same as the mathematics marks by the graphical method.
70, into its corresponding X-mark, draw a horizontal line through 70 on the Y-axis to meet the graph at D. From D draw a perpendicular to the X-axis; this line meets the X-axis at 53 which is the required X-mark. Similarly an X-mark of 30 is converted into a Y-mark by drawing a vertical line at 30 to meet the line at E. From Ε a horizontal line is drawn to meet the Y-axis. This it does at 35. Hence an X-mark of 30 corresponds to a Y-mark of 35. There is no need to draw the horizontal and vertical lines, the position on the graph can be determined by laying a ruler along the appropriate lines.
Standard Deviation For reasons which are beyond the scope of this book to demonstrate, a method is adopted whereby the separate deviations are squared, the mean of these values found and finally the square root taken. The measure thus obtained is called the standard deviation and is the most important of all the measures of variation or dispersion. It is generally denoted by σ (the Greek letter sigma). The calculation of σ is illustrated as follows: d 6 5 4 2 -1 -2 -3 -5 -7 Group A d* 36 25 16 4 1 4 9 25 49 170 Mean 10 Group Β d 19 10 4 3 0 0 -3 -5 -7 -21 2 d 361 100 16 9 0 0 9 25 49 441 1010 17 101 41 10Ό THE SCATTER OF MARKS 39 This method gives a measure which indicates that the scatter of group Β is more than twice that of group A.
Statistics for the Teacher by Douglas M. McIntosh (Auth.)