The monthly revenue collection (in millions of Naira, \text{₦'million}) from six regional … — JAMB UTME

The monthly revenue collection (in millions of Naira, $\text{₦'million}$ ) from six regional revenue offices of a state government was recorded as $14$ , $18$ , $12$ , $x$ , $22$ , and $16$ . If the arithmetic mean of the revenue collected across all six offices is $\text{₦}17\text{ million}$ , what is the value of $x$ ?

Answer: 20 million Naira

Answer

The value of

x

20\text{ million Naira}

(or simply

20

The arithmetic mean is defined as

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

. For

n = 6

offices with a mean of

17\text{ million}

, the total sum must be

6 \times 17 = 102\text{ million}

. Summing the known values gives

14 + 18 + 12 + 22 + 16 = 82

. Subtracting

82

from

102

yields

x = 20\text{ million Naira}

Step-by-Step Solution

Calculate the sum of all observations in terms of

x

Sum

= 14 + 18 + 12 + x + 22 + 16 = 82 + x

The mean formula requires the total sum of all values divided by the number of observations.

Set up the mean equation using

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

\frac{82 + x}{6} = 17

The question specifies that the arithmetic mean across the 6 regional offices is 17.

Solve for the unknown value

x

82 + x = 102 \implies x = 20$

Subtracting the sum of the five known values (82) from the total required sum (102) yields the missing observation.

Key Concept

Calculation of a Missing Value from the Arithmetic Mean

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Step-by-Step Solution

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