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Difficulty: EasyMeasures of Dispersion

The daily temperature readings, in degrees Celsius, recorded over four consecutive days are 1010, 1212, 1414, and 1616. What is the mean deviation of these temperatures?

Answer: 2 °C

Answer

The mean deviation of the temperatures is 2 °C.
To find the mean deviation, first calculate the mean of the data values: (10 + 12 + 14 + 16) / 4 = 13. Next, find the absolute difference of each value from the mean: |10 - 13| = 3, |12 - 13| = 1, |14 - 13| = 1, and |16 - 13| = 3. Finally, average these absolute differences: (3 + 1 + 1 + 3) / 4 = 8 / 4 = 2.

Step-by-Step Solution

1
Calculate the arithmetic mean (average) of the data set
\(\bar{x} = \frac{10 + 12 + 14 + 16}{4} = 13\)
Mean deviation measures dispersion relative to the mean, so the mean must be calculated first.
2
Compute the absolute deviation of each value from the mean
\(|10 - 13| = 3\), \(|12 - 13| = 1\), \(|14 - 13| = 1\), \(|16 - 13| = 3\)
Mean deviation requires non-negative distances of each observation from the mean.
3
Sum the absolute deviations and divide by the sample size (N = 4)
\(\text{Mean Deviation} = \frac{3 + 1 + 1 + 3}{4} = \frac{8}{4} = 2\)
The mean deviation is the average of the absolute deviations.

Key Concept

Mean Deviation for Ungrouped Data
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Topics

Measures of Dispersion

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