Question

the distribution of the number of hours that a random sample of people spend distribution for the data. then use the table to estimate the sample mean and the click the icon to view the pie chart. first construct the frequency distribution. class frequency, f 0 - 4 4 5 - 9 12 10 - 14 25 15 - 19 19 20 - 24 18 25 - 29 14 30+ 4 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 each class

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

Step2: Calculate the product of mid - point and frequency for each class

For the first class: $f_1x_1=4\times2 = 8$; for the second: $f_2x_2=12\times7 = 84$; for the third: $f_3x_3=25\times12 = 300$; for the fourth: $f_4x_4=19\times17 = 323$; for the fifth: $f_5x_5=18\times22 = 396$; for the sixth: $f_6x_6=14\times27 = 378$; for the seventh: $f_7x_7=4\times32 = 128$.

Step3: Find the sum of frequencies

$\sum f_i=4 + 12+25+19+18+14+4=96$.

Step4: Find the sum of the products

$\sum f_ix_i=8 + 84+300+323+396+378+128 = 1617$.

Step5: Calculate the sample mean

$\bar{x}=\frac{\sum f_ix_i}{\sum f_i}=\frac{1617}{96}\approx16.8$.

Answer:

$16.8$