Answer to Question #347797 in Statistics and Probability for Blake

Question

Find the range, variance, and standard deviation unless the question asks for something different.

Police Calls in Schools. The number of incidents in which police were needed for a sample of 10

schools in Allegheny County is 7, 37, 3, 8, 48, 11, 6, 0, 10, 3. Are the data consistent or do they

vary? Explain your answer

Answer 1

Sorted Data Set: 0, 3, 3, 6, 7, 8, 10, 11, 37, 48

$$Range=48-0=48$$

$$mean=\bar{x}=\dfrac{1}{10}(0+3+3+6+7$$

$$+8+10+11+37+48)=13.3$$

$$Var(X)=\sigma^2=\dfrac{\sum_i (x_i-\bar{x})^2}{n}$$

$$=\dfrac{1}{10}(176.89+106.09+106.09+53.29+39.69$$

$$+28.09+10.89+5.29+561.69+1204.09)$$

$$=229.21$$

$$\sigma=\sqrt{\sigma^2}=\sqrt{229.21}=15.139683$$

The standard deviation is small when the data are all concentrated close to the mean, exhibiting little variation or spread. 

We see that the standard deviation is greater than the mean, and this might indicates high variation between values.

The data vary widely.