The table gives the distribution of heights in metres of 100 students.
Height
1.40-1.42
1.43-1.45
1.46-1.48
1.49-1.51
1.52-1.54
1.55-1.57
1.58-1.60
1.61-1.63
Freq
2
4
19
30
24
14
6
1
(a) Calculate the : (i) mean height ; (ii) mean deviation of the distribution. (b) What is the probability that the height of a student selected at random is greater than the mean height of the distribution?
Explanation
Height
ClassMark (x)
1.40-1.42
1.41
2
2.82
-0.1
0.1
0.2
1.43-1.45
1.44
4
5.76
-0.07
0.07
0.28
1.46-1.48
1.47
19
27.93
-0.04
0.04
0.76
1.49-1.51
1.50
30
45.00
-0.01
0.01
0.30
1.52-1.54
1.53
24
36.72
0.02
0.02
0.48
1.55-1.57
1.56
14
21.84
0.05
0.05
0.70
1.58-1.60
1.59
6
9.54
0.08
0.08
0.48
1.61-1.63
1.62
1
1.62
0.11
0.11
0.11
100
151.23
3.31
(a)(i) Mean = (ii) Mean deviation = = = (b) p(height is gretaer than mean height) = =
