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. 20 - 24 17 25 - 29 12 30+ 7 find an approximation for the sample mean. $\bar{x}=square$ (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Find mid - points of intervals

For 20 - 24, mid - point $x_1=\frac{20 + 24}{2}=22$. For 25 - 29, mid - point $x_2=\frac{25+29}{2}=27$. For 30+, mid - point $x_3 = 32$.

Step2: Calculate the sum of products of mid - points and frequencies

Let frequencies be $f_1 = 17$, $f_2=12$, $f_3 = 7$. The sum of products $\sum_{i = 1}^{3}f_ix_i=f_1x_1+f_2x_2+f_3x_3=17\times22+12\times27+7\times32=374 + 324+224 = 922$.

Step3: Calculate the total frequency

The total frequency $n=f_1 + f_2+f_3=17 + 12+7=36$.

Step4: Calculate the sample mean

The sample mean $\bar{x}=\frac{\sum_{i = 1}^{3}f_ix_i}{n}=\frac{922}{36}\approx25.6$.

Answer:

$25.6$