Question

find the mean for the data items in the given frequency distribution. the mean is (round to 3 decimal places as needed.)

Explanation:

Step1: Calculate the product of each score and its frequency

$$\begin{align*} 1\times2&=2\\ 2\times4&=8\\ 3\times3&=9\\ 4\times3&=12\\ 5\times3&=15\\ 6\times2&=12\\ 7\times5&=35\\ 8\times1&=8 \end{align*}$$

Step2: Sum up the products

$$2 + 8+9+12+15+12+35+8=101$$

Step3: Calculate the total frequency

$$2 + 4+3+3+3+2+5+1=23$$

Step4: Calculate the mean

The formula for the mean of a frequency distribution is $\bar{x}=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}$. So, $\bar{x}=\frac{101}{23}\approx4.391$

Answer:

$4.391$