Question

the distribution of the number of hours that a random sample of people spend doing chores per week is shown in the pie chart. use 32 as the midpoint for \30+ hours.\ make a frequency distribution for the data. then use the table to estimate the sample mean and the sample standard deviation of the data set. click the icon to view the pie chart. first construct the frequency distribution. find an approximation for the sample mean. \\( \bar { x } = \square \\) (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate the mid - points of each class

For class \(0 - 4\), mid - point \(x_1=\frac{0 + 4}{2}=2\)
For class \(5 - 9\), mid - point \(x_2=\frac{5+9}{2}=7\)
For class \(10 - 14\), mid - point \(x_3=\frac{10 + 14}{2}=12\)
For class \(15 - 19\), mid - point \(x_4=\frac{15+19}{2}=17\)
For class \(20 - 24\), mid - point \(x_5=\frac{20 + 24}{2}=22\)
For class \(25 - 29\), mid - point \(x_6=\frac{25+29}{2}=27\)
For class \(30+\), mid - point \(x_7 = 32\) (given)

Step2: Calculate the sum of \(f\times x\)

\(\sum(f\times x)=6\times2+9\times7 + 23\times12+18\times17+16\times22+13\times27+5\times32\)
\(=12+63+276+306+352+351+160\)
\(=1520\)

Step3: Calculate the sum of frequencies \(\sum f\)

\(\sum f=6 + 9+23+18+16+13+5=90\)

Step4: Calculate the sample mean \(\bar{x}\)

\(\bar{x}=\frac{\sum(f\times x)}{\sum f}=\frac{1520}{90}\approx16.9\)

Answer:

\(16.9\)