Question

find the range and standard deviation. the table below gives the number of hours spent watching tv last week by a sample of 24 children. 4 7 1 6 1 5 6 7 5 1 1 10 4 7 3 3 1 1 2 4 9 9 8 1 range = 9 (please enter an exact answer.) standard deviation = (please show your answer to 4 decimal places.) enter an integer or decimal number more...

Explanation:

Step1: List all data points

Data: 4,7,1,6,1,5,6,7,5,1,1,10,4,7,3,3,1,1,2,4,9,9,8,1

Step2: Calculate range

Max=10, Min=1, Range=10-1=9

Step3: Compute sample mean

Sum=106, n=24, \( \bar{x}=\frac{106}{24}\approx4.4167 \)

Step4: Sum of squared deviations

\( \sum(x_i-\bar{x})^2\approx203.8333 \)

Step5: Sample variance

\( s^2=\frac{203.8333}{23}\approx8.8623 \)

Step6: Standard deviation

\( s=\sqrt{8.8623}\approx2.9770 \)

Answer:

Range = 9, Standard Deviation = 2.9770