Question

find the mean for the data items in the given frequency distribution.

score, x	1	2	3	4	5	6	7	8	9	10
frequency, f	2	2	1	6	8	9	9	4	3	2

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

Explanation:

Step1: Calculate the product of each score and its frequency

$1\times2 = 2$, $2\times2=4$, $3\times1 = 3$, $4\times6=24$, $5\times8 = 40$, $6\times9=54$, $7\times9 = 63$, $8\times4=32$, $9\times3 = 27$, $10\times2=20$.

Step2: Sum up the products

$2 + 4+3+24+40+54+63+32+27+20=299$.

Step3: Calculate the total frequency

$2 + 2+1+6+8+9+9+4+3+2=46$.

Step4: Calculate the mean

The mean $\bar{x}=\frac{299}{46}\approx6.500$.

Answer:

$6.500$