CHAPTER 11. STATISTICS 11.2
̄−x 3 σ ̄−x 2 σ ̄x−σ ̄x ̄+x σ ̄+2x σ ̄+3x σ68%
95%
99%
What happens if the testwas very easy or very difficult? Then the distribution may not be symmetrical.
If extremely high or extremely low scores are added to a distribution,then the mean tends toshift
towards these scores andthe curve becomes skewed.
If the test was very difficult, the mean score isshifted to the
left. In this case, we saythe distribution is positively skewed,
or skewed right.
If it was very easy, thenmany learners would get high scores,
and the mean of the distribution would be shifted to the right.
We say the distributionis negatively skewed, or skewed left.
Skewed rightSkewed leftExercise 11 - 1
- Given the pairs of normal curves below, sketch the graphs on thesame set of axes and show
any relation between them. An important pointto remember is that thearea beneath the curve
corresponds to 100%.
(a) Mean = 8, standard deviation = 4 and Mean = 4, standard deviation = 8
(b) Mean = 8, standard deviation = 4 and Mean = 16, standard deviation = 4
(c) Mean = 8, standard deviation = 4 and Mean = 8, standard deviation = 8- After a class test, thefollowing scores were recorded:
Test Score Frequency
3 1
4 7
5 14
6 21
7 14
8 6
9 1
Total 64
Mean 6
Standard Deviation 1 , 2(a) Draw the histogramof the results.
(b) Join the midpoints of each bar and draw a frequency polygon.