The table gives the distribution of heights in metres of 100 students. Height 1.40-1.42 1.43-1.45…

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	Class Mark (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)