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.
\

$$\begin{array}{c|c} x & f \\\\ \\hline 1 & 4 \\\\ 2 & 20 \\\\ 3 & 21 \\\\ 4 & 15 \\end{array}$$

the sample mean is \bar{x} = \box
(round to one decimal place as needed.)

Explanation:

Identify the given frequency distribution

Using the Frequency Distribution knowledge point

$$
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$$

Calculate the sample size

Using the Frequency Distribution knowledge point

$$ n = \sum f = 4 + 20 + 21 + 15 = 60 $$

Calculate the sum of products

Using the Mean Calculation knowledge point

$$ \sum (x \cdot f) = (1 \cdot 4) + (2 \cdot 20) + (3 \cdot 21) + (4 \cdot 15) = 4 + 40 + 63 + 60 = 167 $$

Calculate the sample mean

Using the Mean Calculation knowledge point

$$ \bar{x} = \frac{\sum (x \cdot f)}{n} = \frac{167}{60} \approx 2.7833 $$

Rounding to one decimal place:

$$ \bar{x} \approx 2.8 $$

Answer:

The sample mean is \(\bar{x} =\) <blank>\(2.8\)</blank>