the distribution of the tuitions, fees, and room and board charges of a random sample of public 4 - year…

the distribution of the tuitions, fees, and room and board charges of a random sample of public 4 - year degree - granting postsecondary institutions is shown in the pie chart. 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. use $26249.50 as the midpoint for \$25,000 or more.\ complete the frequency distribution for the data. (type integers or decimals. do not round.) class x f $15,000 - $17,499 16249.5 9 $17,500 - $19,999 18749.5 11 $20,000 - $22,499 21249.5 18 $22,500 - $24,999 23749.5 10 $25,000 or more 26249.5 5 the sample mean is x = $ (round to the nearest cent.)

the distribution of the tuitions, fees, and room and board charges of a random sample of public 4 - year degree - granting postsecondary institutions is shown in the pie chart. 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. use $26249.50 as the midpoint for \$25,000 or more.\ complete the frequency distribution for the data. (type integers or decimals. do not round.) class x f $15,000 - $17,499 16249.5 9 $17,500 - $19,999 18749.5 11 $20,000 - $22,499 21249.5 18 $22,500 - $24,999 23749.5 10 $25,000 or more 26249.5 5 the sample mean is x = $ (round to the nearest cent.)

Answer

Explanation:

Step1: Recall sample - mean formula

The formula for the sample mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}$, where $x_i$ is the mid - point of the class and $f_i$ is the frequency of the class. First, calculate $\sum_{i = 1}^{n}x_if_i$: For the first class: $x_1 = 16249.5$, $f_1=9$, so $x_1f_1=16249.5\times9 = 146245.5$ For the second class: $x_2 = 18749.5$, $f_2 = 11$, so $x_2f_2=18749.5\times11=206244.5$ For the third class: $x_3 = 21249.5$, $f_3 = 18$, so $x_3f_3=21249.5\times18 = 382491$ For the fourth class: $x_4 = 23749.5$, $f_4 = 10$, so $x_4f_4=23749.5\times10 = 237495$ For the fifth class: $x_5 = 26249.5$, $f_5 = 5$, so $x_5f_5=26249.5\times5=131247.5$ Then $\sum_{i = 1}^{5}x_if_i=146245.5 + 206244.5+382491+237495+131247.5=1103723.5$

Step2: Calculate the sum of frequencies

$\sum_{i = 1}^{5}f_i=9 + 11+18+10+5=53$

Step3: Calculate the sample mean

$\bar{x}=\frac{\sum_{i = 1}^{5}x_if_i}{\sum_{i = 1}^{5}f_i}=\frac{1103723.5}{53}\approx20824.97$

Answer:

$20824.97$