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Mathematics

The following are the marks obtained by 70 boys in a class test.

MarksNo. of boys
30 - 4010
40 - 5012
50 - 6014
60 - 7012
70 - 809
80 - 907
90 - 1006

Calculate the mean by :

(i) Short-cut method

(ii) Step-deviation method

Measures of Central Tendency

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Answer

(i) Let assumed mean (A) be 65.

MarksMid value (x)No. of boys (f)d = x - Afd
30 - 40351035 - 65 = -30-300
40 - 50451245 - 65 = -20-240
50 - 60551455 - 65 = -10-140
60 - 70651265 - 65 = 00
70 - 8075975 - 65 = 1090
80 - 9085785 - 65 = 20140
90 - 10095695 - 65 = 30180
TotalΣf = 70Σfx = -270

n = Σf = 70.

By formula,

Mean = A + Σfdn=65+−27070\dfrac{Σfd}{n} = 65 + \dfrac{-270}{70}

= 65 - 3.86 = 61.14

Hence, mean = 61.14

(ii) We get mean values from part (i) and assumed mean (A) = 65. Let i = 10.

MarksMid value (x)No. of boys (f)d = x - At = (x - A)/ift
30 - 40351035 - 65 = -30-3-30
40 - 50451245 - 65 = -20-2-24
50 - 60551455 - 65 = -10-1-14
60 - 70651265 - 65 = 000
70 - 8075975 - 65 = 1019
80 - 9085785 - 65 = 20214
90 - 10095695 - 65 = 30318
TotalΣf = 70Σft = -27

n = Σf = 70.

By formula,

Mean = A + Σftn×i\dfrac{Σft}{n} \times i

= 65 + −2770×10\dfrac{-27}{70} \times 10

= 65 - 277\dfrac{27}{7}

= 65 - 3.86

= 61.14

Hence, mean = 61.14

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