Question

The following data show the number of hours spent watching television for 10 randomly selected freshmen attending a liberal arts college in the Midwest. Hours of Television Viewed Weekly 12 17 19 15 12 18 11 15 12 12 Calculate the​ range, variance, standard​ deviation, and interquartile range for the sample data. The range for the data set is nothing. ​(Type an integer or a decimal. Do not​ round.) The sample​ variance, s squared​, is nothing. ​(Round to two decimal places as​ needed.)

Answer 1

Answer:

Range = 19-11 = 13

Median = (12+15)/2 = 13.5

Mean = 14.3

IQR = 5

Variance = 8.45

Standard​ deviation = 2.907

Explanation:

12 17 19 15 12 18 11 15 12 12

Arranging in ascending order

11 12 12 12 12 15 15 17 18 19

Range = 19-11 = 13

Median = (12+15)/2 = 13.5

$Q_1=12$

$Q_3=17$

Interquartile range

$IQR=Q_3-Q_1\\\Rightarrow IQR=17-12\\\Rightarrow IQR=5$

Interquartile range is 5

Mean

$\bar{x}=\frac{12+17+19+15+12+18+11+15+12+12}{10}\\\Rightarrow \bar{x}=14.3$

$v=\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\bar{x})^2\\\Rightarrow v=\frac{1}{9}\times 76.1\\\Rightarrow v=8.45$

Variance = 8.45

$s=\sqrt v\\\Rightarrow s=\sqrt{8.45}\\\Rightarrow s=2.907$

Standard​ deviation = 2.907