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 2 2 2 3 5 3 6 2 the mean is (round to 3 decimal places as needed.)

Explanation:

Step1: Calculate the product of each score and its frequency

$1\times2 = 2$, $2\times2=4$, $3\times2 = 6$, $4\times3=12$, $5\times5 = 25$, $6\times3=18$, $7\times6 = 42$, $8\times2=16$

Step2: Sum up the products

$2 + 4+6 + 12+25+18+42+16=125$

Step3: Calculate the total frequency

$2+2 + 2+3+5+3+6+2=25$

Step4: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_if_i}{\sum_{i = 1}^{n}f_i}=\frac{125}{25}=5.000$

Answer:

$5.000$