Mathematics

Mathematics

Problem

The temperature deviations from the average (in ∘^{\circ}C) recorded in a city over 12 consecutive days were: −1.5,  0.3,  1.2,  −0.8,  0.0,  1.7,  −1.1,  0.9,  −0.2,  1.4,  −0.9,  0.0-1.5,\;0.3,\;1.2,\;-0.8,\;0.0,\;1.7,\;-1.1,\;0.9,\;-0.2,\;1.4,\;-0.9,\;0.0. Solve the following. a. (i) Compute the mean temperature deviation. b. (ii) Determine the variance of the deviations. c. (iii) Hence find the standard deviation, correct to two decimal places.
Intuitive explanation

This problem asks you to work with deviations from a mean—differences that show how far each measurement strays from the average. The key insight is that deviations are already centered around zero, so their sum should be close to zero (any small difference reveals rounding or measurement error). Use this property to check your work, and organize the data by sign to spot patterns in warming versus cooling days.

Intuitive explanation

This problem asks you to work with deviations from a mean—differences that show how far each measurement strays from the average. The key insight is that deviations are already centered around zero, so their sum should be close to zero (any small difference reveals rounding or measurement error). Use this property to check your work, and organize the data by sign to spot patterns in warming versus cooling days.

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