Question

Following is an incomplete distribution having modal mark as 44

Marks: 0–20 20–40 40–60 60–80 80–100

No. of Students: 5 18 ? 12 5

What would be the mean marks?​

Answer 1

The mean marks of the given data is 48

Given:-

Mode = 44

Marks: 0-20, 20-40, 40-60, 60-80, 80-100

No of Students: 5 18 ? 12 5

To Find:-

Mean marks of the given data

Solution:-

Since the mode of the given data is 44, the modal class of the given data is 40-60.

Mode =$L+h(\frac{(f_{m}-f_{1}) }{(2f_{m}-f_{1}-f_{2}) }$

⇒44 = 40 + ((x-18)/(x-18)+(x+12)) 20

⇒4/20 = x-18/2x-30

⇒3x = 60

⇒x = 20

∴The missing value is 20. We can thus find the sum which is,

Sum = 10x5 + 30x18 + 50x20 + 70x12 + 90x15

⇒Sum = 2880

∴Mean = 2880/60

⇒Mean = 48

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