a survey was conducted by education minister India the following distribution gives the state wise teachers students ratio in in higher secondary schools of India
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Given : survey was conducted by education minister India the following distribution gives the state wise teachers students ratio in in higher secondary schools of India
15 - 20 3
20 - 25 8
25 - 30 9
30 - 35 10
35 - 40 3
40 - 45 0
45 - 50 0
50 - 55 2
To Find : Mean
Modal class
Mode
Solution :
Class f cf Mean A=(mean - 32.5)/5 Af
15 - 20 3 3 17.5 -3 -9
20 - 25 8 11 22.5 -2 - 16
25 - 30 9 20 27.5 -1 -9
30 - 35 10 30 32.5 0 0
35 - 40 3 33 37.5 1 3
40 - 45 0 33 42.5 2 0
45 - 50 0 33 47.5 3 0
50 - 55 2 35 52.5 4 8
35 -23
Mean = 32.5 + 5 * ( -23)/35
= 29.214
= 29.2
Modal Class = 30 - 35 ( as it has max frequency 10)
Mode = 30 + 5 x (10 - 9)/(10 - 9 + 10 - 3)
= 30 + 5/8
= 30.625
Median = 25 + 5 x ( 17.5 - 11)/9
= 25 + 3.61
= 28.61
CF table is useful to find median
( half of upper class limit + lower class limit)/2 = class Mark
The class midpoint (or class mark)
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Step-by-step explanation:
(a) option b I.e. 30-35
(b) option d I.e 29.21
(c) option b I.e. 30.625
(d) option b I.e. classmark
(e) option c I.e. median