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)
\(f\)
\(fx\)
\(d = x - \bar{x}\)
\(|d|\)
\(fd\)
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 \(\bar{x} = \frac{\sum fx}{\sum f}\) = \(\frac{151.23}{100}\) \(\approxeq 1.51cm\) (ii) Mean deviation = \(\frac{\sum fd}{\sum f}\) = \(\frac{3.31}{100}\) = \(0.033\) (b) p(height is gretaer than mean height) = \(\frac{24 + 14 + 6 + 1}{100}\) = \(0.45\)
