The reported mean monthly wage of 50 employees in a manufacturing firm was recorded as 42 … — JAMB UTME

The reported mean monthly wage of $50$ employees in a manufacturing firm was recorded as $42$ (in thousands of Naira, $\text{₦'000}$ ). During an internal audit, two transcription errors were discovered: a wage of $\text{₦}64,000$ was incorrectly recorded as $\text{₦}46,000$ , and a wage of $\text{₦}28,000$ was incorrectly recorded as $\text{₦}82,000$ . Additionally, $10$ new workers were recruited at an average monthly wage of $\text{₦}57,000$ (recorded as $57$ in $\text{₦'000}$ ). What is the corrected mean monthly wage (in $\text{₦'000}$ ) for the entire workforce of $60$ employees?

Answer: 43.9 ₦'000

Answer

The corrected mean monthly wage for the entire workforce of 60 employees is 43.9 in thousands of Naira (₦'000), which represents ₦43,900.

The initial reported wage sum of ₦2,100,000 (

2100

\text{₦'000}

) is adjusted by adding

\text{₦}18,000

for the under-recorded entry and subtracting

\text{₦}54,000

for the over-recorded entry, giving a corrected baseline sum of

\text{₦}2,064,000

(

2064

\text{₦'000}

). Adding the

\text{₦}570,000

(

570

\text{₦'000}

) earned by the

10

new recruits gives a total aggregate wage sum of

\text{₦}2,634,000

(

2634

\text{₦'000}

) across

60

total employees. Dividing

2634

60

gives an exact corrected mean of

43.9

\text{₦'000}

(or

\text{₦}43,900

Step-by-Step Solution

Find initial reported total wage expenditure

50 × 42 = 2100 (in ₦'000)

Total value equals sample size multiplied by reported arithmetic mean.

Calculate net error adjustment

(64 - 46) + (28 - 82) = +18 - 54 = -36 (in ₦'000)

Under-recorded item adds +18, while over-recorded item subtracts -54.

Adjust initial total wage expenditure

2100 - 36 = 2064 (in ₦'000)

Correcting errors adjusts the sum of the original 50 workers' wages.

Calculate wage expenditure of new workers

10 × 57 = 570 (in ₦'000)

Total earnings of additional workers equal number of recruits times their mean wage.

Compute total combined expenditure and workforce size

Total sum = 2064 + 570 = 2634 (in ₦'000); Total N = 50 + 10 = 60

Combine corrected original wage sum with new recruitment total.

Calculate final corrected combined mean

2634 / 60 = 43.9 (in ₦'000)

Divide aggregate wage sum by aggregate total number of employees.

Key Concept

Corrected Mean and Weighted Combined Mean

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