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Mathematics

For the given frequency distribution, find the:
(a) mean, to the nearest whole number
(b) median
x f
10 3
11 2
12 2
13 6
14 3
15 5
16 3

Measures of Central Tendency

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Answer

x	f	fx
10	3	30
11	2	22
12	2	24
13	6	78
14	3	42
15	5	75
16	3	48
Total	Σf = 24	Σfx = 319

(a) By formula,

$\text{Mean} = \dfrac{\sum fx}{\sum f} = \dfrac{319}{24} = 13.291…\approx 13.$

Hence, required mean = 13.

(b) Cumulative frequency table :

x	f	cf
10	3	3
11	2	5 (3 + 2)
12	2	7 (5 + 2)
13	6	13 (7 + 6)
14	3	16 (13 + 3)
15	5	21 (16 + 5)
16	3	24 (21 + 3)

Median

Here, total frequency (N) = 24 and $\dfrac{N}{2} = 12$ .

From the cumulative column,

For 8th to 13th term, the value of x = 13.

Hence, median = 13.

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