The table shows the distribution of the heights of a group of people. Height (m)…

The table shows the distribution of the heights of a group of people.

Height (m)	0.4 – 0.5	0.6 – 0.9	1.0 – 1.2	1.3 – 1.4	1.5 – 1.7
Number of people	2	8	12	6	6

(a) Draw a histogram to illustrate the distribution.

(b) Using an assumed mean of 1.1m, find, correct to one decimal place, the mean height of the group.

Explanation

Height (m)	frequency	boundaries	freq. density
0.4 – 0.5	2	0.35 – 0.55	10
0.6 – 0.9	8	0.55 – 0.95	20
1.0 – 1.2	12	0.95 – 1.25	40
1.3 – 1.4	6	1.25 – 1.45	30
1.5 – 1.7	6	1.45 – 1.75	20

(a) 

(b) Assumed mean = 1.1m

Height (m)	mid-height x	Frequency	(d = x – A)	(fd)
0.4 – 0.5	0.45	2	-0.65	-1.3
0.6 – 0.9	0.75	8	-0.35	-2.8
1.0 – 1.2	1.10	12	0	0
1.3 – 1.4	1.35	6	0.25	1.5
1.5 – 1.7	1.60	6	0.5	3.0
		34		0.4

(Mean = A + frac{sum fd}{N})

= (1.1 + frac{0.4}{34})

= (1.1 + 0.0118)

= (1.1118)

(approxeq 1.1) (to 1 d.p)