Questions: Use the display of data to find the standard deviation. The standard deviation is approximately □. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Solution Steps

From the histogram, we can extract the following data points:

• Score 6: Frequency 4
• Score 7: Frequency 6
• Score 8: Frequency 10
• Score 9: Frequency 6
• Score 10: Frequency 4

Calculate the mean (average) of the scores. \[ \text{Mean} = \frac{\sum (\text{Score} \times \text{Frequency})}{\sum \text{Frequency}} \] \[ \text{Mean} = \frac{(6 \times 4) + (7 \times 6) + (8 \times 10) + (9 \times 6) + (10 \times 4)}{4 + 6 + 10 + 6 + 4} \] \[ \text{Mean} = \frac{24 + 42 + 80 + 54 + 40}{30} = \frac{240}{30} = 8 \]

Calculate the variance using the formula: \[ \text{Variance} = \frac{\sum (\text{Frequency} \times (\text{Score} - \text{Mean})^2)}{\sum \text{Frequency}} \] \[ \text{Variance} = \frac{4(6-8)^2 + 6(7-8)^2 + 10(8-8)^2 + 6(9-8)^2 + 4(10-8)^2}{30} \] \[ \text{Variance} = \frac{4(4) + 6(1) + 10(0) + 6(1) + 4(4)}{30} \] \[ \text{Variance} = \frac{16 + 6 + 0 + 6 + 16}{30} = \frac{44}{30} \approx 1.47 \]

The standard deviation is the square root of the variance. \[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{1.47} \approx 1.21 \]

Final Answer