Question

The standard deviation for the following scores: 8, 6, 6, 9, 6, 5, 6, 2 is \(\_\_\_\_\_\_\) (rounded off to two decimal places).

Hint:

Standard deviation measures data spread around the mean and is a crucial statistic for variability.

Answer 1

The steps to calculate the standard deviation are as follows:
1. Calculate the Mean \[ \text{Mean} = \frac{8 + 6 + 6 + 9 + 6 + 5 + 6 + 2}{8} = \frac{48}{8} = 6 \] 2. Calculate the Squared Differences from the Mean \[ (8 - 6)^2 = 4, \quad (6 - 6)^2 = 0, \quad (6 - 6)^2 = 0, \quad (9 - 6)^2 = 9, \] \[ (6 - 6)^2 = 0, \quad (5 - 6)^2 = 1, \quad (6 - 6)^2 = 0, \quad (2 - 6)^2 = 16 \]
3. Sum of squared differences:
\[ 4 + 0 + 0 + 9 + 0 + 1 + 0 + 16 = 30 \]
4. Calculate the variance:
\[ \text{Variance} = \frac{\text{Sum of squared differences}}{\text{Number of observations}} = \frac{30}{8} = 3.75 \]
5. Calculate the standard deviation:
\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{3.75} \approx 1.92 \]
Thus, the standard deviation for the given data is 1.92.