Question

the numbers of courses taught per semester by a random sample of university professors are shown in the histogram. 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. make a frequency distribution for the data. x f 1 3 2 16 3 22 4 14 the sample mean is x = (round to one decimal place as needed.)

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 value of the variable and $f_i$ is the frequency.
First, calculate $\sum_{i = 1}^{n}x_if_i$ and $\sum_{i = 1}^{n}f_i$.
$\sum_{i = 1}^{n}f_i=3 + 16+22 + 14=55$.
$\sum_{i = 1}^{n}x_if_i=1\times3+2\times16 + 3\times22+4\times14$.

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

$1\times3+2\times16 + 3\times22+4\times14=3+32 + 66+56=157$.

Step3: Calculate the sample - mean

$\bar{x}=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}=\frac{157}{55}\approx2.9$.

Answer:

$2.9$