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Difficulty: MediumMeasures of Central Tendency

The mean daily production cost of five small poultry farms in Ogun State is ₦45,000\text{₦}45,000. If the daily production costs of four of the farms are ₦38,000\text{₦}38,000, ₦42,000\text{₦}42,000, ₦46,000\text{₦}46,000, and ₦50,000\text{₦}50,000, what is the daily production cost (in ₦\text{₦}) of the fifth farm?

Answer: 49000 ₦

Answer

The daily production cost of the fifth farm is ₦49,000\text{₦}49,000.
The arithmetic mean formula is Xˉ=∑XN\bar{X} = \frac{\sum X}{N}. For 5 farms with a mean of ₦45,000\text{₦}45,000, the total combined cost is 5×₦45,000=₦225,0005 \times \text{₦}45,000 = \text{₦}225,000. Summing the four given farm costs yields ₦38,000+₦42,000+₦46,000+₦50,000=₦176,000\text{₦}38,000 + \text{₦}42,000 + \text{₦}46,000 + \text{₦}50,000 = \text{₦}176,000. The cost for the fifth farm is ₦225,000−₦176,000=₦49,000\text{₦}225,000 - \text{₦}176,000 = \text{₦}49,000.

Step-by-Step Solution

1
Calculate total production cost of all 5 farms
Total cost = ₦225,000\text{₦}225,000
Using the arithmetic mean formula Xˉ=∑XN\bar{X} = \frac{\sum X}{N}, the total sum ∑X=N×Xˉ=5×45,000=225,000\sum X = N \times \bar{X} = 5 \times 45,000 = 225,000.
2
Sum the daily production costs of the four known farms
Known total = ₦176,000\text{₦}176,000
38,000+42,000+46,000+50,000=176,00038,000 + 42,000 + 46,000 + 50,000 = 176,000.
3
Determine the unknown fifth farm cost by subtraction
Fifth farm cost = ₦49,000\text{₦}49,000
Subtracting the sum of the four known values from the overall total: 225,000−176,000=49,000225,000 - 176,000 = 49,000.

Key Concept

Calculating a missing value using the total sum property of the arithmetic mean
Estimated Time:1m 15s
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Topics

Measures of Central Tendency

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