Question

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.

(type integers or decimals. do not round.)

class\t$15,000 - $17,499\t$17,500 - $19,999\t$20,000 - $22,499\t$22,500 - $24,999\t$25,000 or more
x\t16249.5\t18749.5\t21249.5\t23749.5\t26249.5
t\t8\t12\t17\t10\t5

the sample mean is x =

Explanation:

Step1: Recall the formula for sample - mean

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 $\sum_{i = 1}^{n}x_if_i$ and $\sum_{i = 1}^{n}f_i$.

Step2: Calculate $\sum_{i = 1}^{n}x_if_i$

For the first class ($15000 - 17499$) with $x_1 = 16249.5$ and $f_1=8$, $x_1f_1=16249.5\times8 = 129996$.
For the second class ($17500 - 19999$) with $x_2 = 18749.5$ and $f_2 = 12$, $x_2f_2=18749.5\times12=224994$.
For the third class ($20000 - 22499$) with $x_3 = 21249.5$ and $f_3 = 17$, $x_3f_3=21249.5\times17 = 361241.5$.
For the fourth class ($22500 - 24999$) with $x_4 = 23749.5$ and $f_4 = 10$, $x_4f_4=23749.5\times10 = 237495$.
For the fifth class ($25000$ or more) with $x_5 = 26249.5$ and $f_5 = 5$, $x_5f_5=26249.5\times5=131247.5$.
$\sum_{i = 1}^{5}x_if_i=129996 + 224994+361241.5+237495+131247.5=1084974$.

Step3: Calculate $\sum_{i = 1}^{n}f_i$

$\sum_{i = 1}^{5}f_i=8 + 12+17+10+5=52$.

Step4: Calculate the sample mean

$\bar{x}=\frac{\sum_{i = 1}^{5}x_if_i}{\sum_{i = 1}^{5}f_i}=\frac{1084974}{52}\approx20864.88$.

Answer:

$20864.88$