An agricultural economist recorded the prices per bag of fertilizer (in thousands of Naira… — JAMB UTME

An agricultural economist recorded the prices per bag of fertilizer (in thousands of Naira) across five regional markets as $₦12$ , $₦15$ , $₦18$ , $₦21$ , and $₦24$ . What is the mean deviation of the fertilizer prices (in thousands of Naira)?

Answer: 3.6 thousand Naira

Answer

The mean deviation of the fertilizer prices is

3.6

thousand Naira.

The mean deviation is

3.6

because the arithmetic mean of the prices is

18

. The absolute differences of the data values from

18

are

6

3

0

3

, and

6

. The sum of these absolute deviations is

18

, and dividing by

5

observations yields

3.6

Step-by-Step Solution

Calculate the arithmetic mean (

\bar{x}

) of the data set

\bar{x} = \frac{12 + 15 + 18 + 21 + 24}{5} = \frac{90}{5} = 18

The arithmetic mean provides the central reference point required to evaluate individual deviations.

Determine the absolute deviation

|x - \bar{x}|

for each value

|12 - 18| = 6

|15 - 18| = 3

|18 - 18| = 0

|21 - 18| = 3

|24 - 18| = 6

Mean deviation measures dispersion using absolute differences to prevent positive and negative deviations from canceling out.

Compute the average of the absolute deviations

\text{Mean Deviation} = \frac{6 + 3 + 0 + 3 + 6}{5} = \frac{18}{5} = 3.6

Dividing the sum of absolute deviations by the total number of observations gives the mean deviation.

Key Concept

Mean Deviation

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