Q12

Given Data

32, 32, 30, 35, 33, 34, 28, 29, 30, 31, 31, 29, 30, 31, 32, 31, 31, 28, 28, 31, 28, 28, 33, 31, 32, 38, 39

Total observations: \( n = 27 \)

Frequency Table

Value (x)	Frequency (f)
28	5
29	2
30	3
31	7
32	4
33	2
34	1
35	1
38	1
39	1

Mode

Highest frequency = 7

$$ \text{Mode} = 31 $$

Median

$$ \text{Median position} = \frac{n+1}{2} $$

$$ = \frac{27+1}{2} = \frac{28}{2} = 14^{th}\ \text{observation} $$

The 14th observation lies in 31.

$$ \text{Median} = 31 $$

$$ \text{Mean} = \frac{\sum fx}{\sum f} $$

x	f	fx
28	5	140
29	2	58
30	3	90
31	7	217
32	4	128
33	2	66
34	1	34
35	1	35
38	1	38
39	1	39

$$ \sum fx = 845 $$

$$ \sum f = 27 $$

$$ \text{Mean} = \frac{845}{27} = 31 + \frac{8}{27} $$

$$ \text{Mean} \approx 31.30 $$

$$ \text{Range} = \text{Maximum value} – \text{Minimum value} $$

$$ = 39 – 28 = 11 $$