Question

math ii
standard deviation worksheet name
find the range and standard deviation of the data set.

1. 22, 18, 19, 25, 27, 21, 24

Explanation:

Step1: Calculate range

Range = Max - Min = 27 - 18 = 9

Step2: Find mean

Mean $\mu = \frac{22+18+19+25+27+21+24}{7} = \frac{156}{7} \approx 22.2857$

Step3: Compute squared deviations

$(22-22.2857)^2 \approx 0.0816$, $(18-22.2857)^2 \approx 18.3673$, $(19-22.2857)^2 \approx 10.7959$, $(25-22.2857)^2 \approx 7.3673$, $(27-22.2857)^2 \approx 22.2245$, $(21-22.2857)^2 \approx 1.6531$, $(24-22.2857)^2 \approx 2.9469$

Step4: Calculate variance

Variance $\sigma^2 = \frac{0.0816+18.3673+10.7959+7.3673+22.2245+1.6531+2.9469}{7} \approx \frac{63.4366}{7} \approx 9.0624$

Step5: Find standard deviation

Standard deviation $\sigma = \sqrt{9.0624} \approx 3.01$

Answer:

Range: 9; Standard Deviation: ≈3.01