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 4 3 3 4 2 2 3
the mean is . (round to 3 decimal places as needed.)

Explanation:

Step1: Calculate the product of each score and its frequency

$1\times2 = 2$, $2\times4=8$, $3\times3 = 9$, $4\times3=12$, $5\times4 = 20$, $6\times2=12$, $7\times2 = 14$, $8\times3=24$.

Step2: Sum up the products

$2 + 8+9+12+20+12+14+24=101$.

Step3: Sum up the frequencies

$2 + 4+3+3+4+2+2+3=23$.

Step4: Calculate the mean

The mean $\bar{x}=\frac{101}{23}\approx4.391$.

Answer:

$4.391$