The table below shows the distribution of weekly expenditures (in thousands of Naira, ₦'000) of a group of market traders: | Expenditure (₦'000) | Frequency (f) | |---|---| | 10 | 5 | | 20 | 8 | | 30 | x | | 40 | 4 | | 50 | 3 | If the mean weekly expenditure of the traders is ₦28,000 (represented as

The table below shows the distribution of weekly expenditures (in thousands of Naira, ₦'00… — JAMB UTME

The table below shows the distribution of weekly expenditures (in thousands of Naira, ₦'000) of a group of market traders:

If the mean weekly expenditure of the traders is ₦28,000 (represented as $28$ in the table units), find the value of $x$ .

Answer: 20

The value of

x

is 20.

Using the arithmetic mean formula

\bar{x} = \frac{\sum fx}{\sum f}

, we set up the equation with the given mean of 28:

\frac{520 + 30x}{20 + x} = 28

. Cross-multiplying gives

520 + 30x = 560 + 28x

. Rearranging terms yields

2x = 40

, which gives

x = 20

Sum all given frequencies including the unknown

x

to get the total frequency expression.

\sum f = 20 + x

The total number of observations is needed for the denominator of the arithmetic mean formula.

Multiply each expenditure value by its respective frequency and aggregate the terms.

\sum f x = 520 + 30x

The total weighted value of all expenditures is needed for the numerator of the mean formula.

Substitute the known mean value of 28 into the equation

\bar{x} = \frac{\sum f x}{\sum f}

and solve for

x

x = 20

Isolating

x

yields the exact missing frequency.

Finding a missing frequency from a frequency distribution given the arithmetic mean.