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The following distribution shows the daily pocket allowance of children of a locality.The mean pocket allowance is Rs 18.Find the missing frequency?
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The following distribution shows the daily pocket allowance of childre...
Calculation of Missing Frequency in Pocket Allowance Distribution


Given Data:


  • Mean pocket allowance = Rs 18

  • Other frequencies and their corresponding pocket allowances are given in the table below

  • One of the frequencies is missing






















Pocket Allowance 10 12 14 16 20 22
Frequency 5 10 15 20 ? 5


Formula for Mean:

$$ Mean = \frac{\sum f_i \times x_i}{\sum f_i} $$

where,

$f_i$ = frequency of the i-th class

$x_i$ = midpoint of the i-th class

Calculation of Missing Frequency:

Let the missing frequency be 'm'.

Using the formula for mean, we can write:

$$ 18 = \frac{(5 \times 10) + (10 \times 12) + (15 \times 14) + (20 \times 16) + (m \times 20) + (5 \times 22)}{f} $$

where, 'f' is the total frequency (including the missing frequency)

Simplifying the above equation, we get:

$$ 18f = 1220 + 20m $$

Substituting the given values, we get:

$$ 18(f-1) = 1220 + 20 \times 22 $$

$$ 18f - 18 = 1660 $$

$$ 18f = 1678 $$

$$ f = 93.22 $$

Since 'f' represents the total frequency, it should be a whole number. Therefore, the missing frequency can be calculated as:

$$ m = \frac{18f - 1220}{20} $$

$$ m = \frac{(18 \times 93) - 1220}{20} $$

$$ m = 11.25 $$

Since the missing frequency must be a whole number, the closest whole number to 11.25 is 11.

Therefore, the missing frequency is 11.
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The following distribution shows the daily pocket allowance of children of a locality.The mean pocket allowance is Rs 18.Find the missing frequency?
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