The ages, in years, of five participants in a workshop are 2, 4, 5, 7, and 12. What is the… — JAMB UTME

The ages, in years, of five participants in a workshop are $2, 4, 5, 7,$ and $12$ . What is the mean deviation of the ages?

2.8

The mean deviation is calculated by taking the average of the absolute differences between each data point and the mean. For the dataset

2, 4, 5, 7,

and

12

, the mean is

6

. The absolute deviations from

6

are

4, 2, 1, 1,

and

6

, which sum to

14

. Dividing

14

5

gives

2.8

Calculate the arithmetic mean (

\bar{x}

) of the dataset.

\bar{x} = \frac{2 + 4 + 5 + 7 + 12}{5} = \frac{30}{5} = 6

The mean is needed as the reference point to calculate deviations.

Calculate the absolute deviation

|x - \bar{x}|

for each data item.

|2 - 6| = 4, \quad |4 - 6| = 2, \quad |5 - 6| = 1, \quad |7 - 6| = 1, \quad |12 - 6| = 6

Mean deviation measures distance from the mean, so absolute values are taken.

Find the average of these absolute deviations.

\text{Mean Deviation} = \frac{4 + 2 + 1 + 1 + 6}{5} = \frac{14}{5} = 2.8

The formula for mean deviation of ungrouped data is

\frac{\sum |x - \bar{x}|}{n}

Mean Deviation for Ungrouped Data

Question