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Mathematics

The following table gives the weekly wages (in ₹) of workers in a factory :

Weekly wages (in ₹)No. of workers
50 - 555
55 - 6020
60 - 6510
65 - 7010
70 - 759
75 - 806
80 - 8512
85 - 908

Calculate :

(i) the mean.

(ii) the modal class.

(iii) the number of workers getting weekly wages below ₹80.

(iv) the number of workers getting ₹65 or more but less than ₹85 as weekly wages.

Measures of Central Tendency

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Answer

We construct the following table :

Weekly wages (xi)No. of workers (fi)Class Mark (ui)Cumulative frequency (C.F.)fiui
50 - 55552.55262.5
55 - 602057.5251150
60 - 651062.535625
65 - 701067.545675
70 - 75972.554652.5
75 - 80677.560465
80 - 851282.572990
85 - 90887.580700
Total805520

(i) Mean = fiuifi=552080\dfrac{∑fiui}{∑f_i} = \dfrac{5520}{80} = 69.

Hence, mean = 69.

(ii) The class 55 - 60 has maximum frequency 20.

Hence, modal class is 55 - 60.

(iii) From table,

The number of workers getting weekly wages below ₹80 = 60.

(iv) From table,

The number of workers getting ₹65 or more but less than ₹85 as weekly wages = 72 - 35 = 37.

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