The table below shows the frequency distribution of marks obtained by a group of students in a mathematics test: | Mark (x) | 2 | 4 | 6 | 8 | 10 | |---|---|---|---|---|---| | Frequency (f) | 2 | 1 | 4 | 1 | 2 | Find the mean deviation of the distribution.

The table below shows the frequency distribution of marks obtained by a group of students … — JAMB UTME

The table below shows the frequency distribution of marks obtained by a group of students in a mathematics test:

Mark ( $x$ )	2	4	6	8	10
Frequency ( $f$ )	2	1	4	1	2

Find the mean deviation of the distribution.

Answer: 2

Answer

The mean deviation of the distribution is 2.

To find the mean deviation, first calculate the mean

\bar{x} = \frac{\sum fx}{\sum f} = \frac{60}{10} = 6

. Next, sum the absolute deviations multiplied by their frequencies:

\sum f|x - \bar{x}| = 2(4) + 1(2) + 4(0) + 1(2) + 2(4) = 20

. Dividing this total by the sum of frequencies

10

yields a mean deviation of

2

Step-by-Step Solution

Calculate the arithmetic mean of the distribution

\bar{x} = \frac{\sum f x}{\sum f} = \frac{(2 \times 2) + (1 \times 4) + (4 \times 6) + (1 \times 8) + (2 \times 10)}{2 + 1 + 4 + 1 + 2} = \frac{60}{10} = 6

The mean is required as the central benchmark from which individual deviations are measured.

Calculate the sum of absolute deviations weighted by frequency

\sum f |x - \bar{x}| = 2|2 - 6| + 1|4 - 6| + 4|6 - 6| + 1|8 - 6| + 2|10 - 6| = 8 + 2 + 0 + 2 + 8 = 20

Each absolute difference from the mean must be multiplied by its frequency to account for the total deviation.

Divide the total absolute deviation by the total frequency

\text{Mean Deviation} = \frac{\sum f |x - \bar{x}|}{\sum f} = \frac{20}{10} = 2

The mean deviation represents the average distance of all observations from the arithmetic mean.

Key Concept

Mean Deviation of a Frequency Distribution

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