Question

find the mean for the data items in the given frequency distribution.
score, x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
frequency, f | 3 | 4 | 2 | 6 | 4 | 4 | 3 | 3
the mean is \boxed{}. (round to 3 decimal places as needed.)

Explanation:

Step1: Calculate the product of each score and its frequency

$$\begin{align*} 1\times3&=3\\ 2\times4&=8\\ 3\times2&=6\\ 4\times6&=24\\ 5\times4&=20\\ 6\times4&=24\\ 7\times3&=21\\ 8\times3&=24 \end{align*}$$

Step2: Sum up the products

$$3 + 8+6 + 24+20+24+21+24=120$$

Step3: Calculate the total frequency

$$3 + 4+2 + 6+4+4+3+3=29$$

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, $\bar{x}=\frac{120}{29}\approx4.138$

Answer:

$4.138$