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Question

The arithmetic mean of the following frequency distribution is 47. Determine the value of p.

Class-interval0-2020-4040-6060-8080-100
Frequency81520p5

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Solution

Step 1 Finding mean:

Completing the table,

Class-intervalMid-value xiFrequency fifixi
0-2010880
20-403015450
40-6050201000
60-8070p70p
80-100905450
Σfi=48+pΣfixi=1980+70p

The formula for mean is x¯=ΣfixiΣfi.

where Σfi is the total frequency and xi is the mid-value of class-intervals.

From the question, we have x¯=47.

Step 2: Finding the value of p:

Substituting the values in the formula for mean,

47=1980+70p48+p2256+47p=1980+70p23p=276p=12

Hence, the value of p is obtained as 12.


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