A meteorologist recorded the rainfall (in millimeters) in a town over five days as 2, 5, 6… — JAMB UTME

A meteorologist recorded the rainfall (in millimeters) in a town over five days as $2$ , $5$ , $6$ , $7$ , and $10$ . What is the mean deviation of the rainfall data?

$2$ Answer
B
$0$
C
$10$
D
$6$

Answer

The mean deviation of the rainfall data is

2

To find the mean deviation, first calculate the mean of the data:

(2 + 5 + 6 + 7 + 10) / 5 = 6

. Next, calculate the absolute difference of each value from 6, which yields 4, 1, 0, 1, and 4. The average of these absolute differences is

(4 + 1 + 0 + 1 + 4) / 5 = 10 / 5 = 2

Step-by-Step Solution

Calculate the arithmetic mean (

\bar{x}

) of the dataset.

\bar{x} = \frac{2 + 5 + 6 + 7 + 10}{5} = \frac{30}{5} = 6

The mean is required to compute the deviation of each observation from the central value.

Find the absolute deviation

|x - \bar{x}|

for each data point.

|2 - 6| = 4, \quad |5 - 6| = 1, \quad |6 - 6| = 0, \quad |7 - 6| = 1, \quad |10 - 6| = 4

Mean deviation measures the average absolute distance of data values from the mean.

Sum the absolute deviations and divide by the total number of observations (

N = 5

\text{Mean Deviation} = \frac{4 + 1 + 0 + 1 + 4}{5} = \frac{10}{5} = 2

Dividing the sum of absolute deviations by

N

gives the mean deviation.

Key Concept

Mean Deviation

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