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Math  /  Data & Statistics

QuestionFind the mean for the data items in the given frequency distribution. \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Score, x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Frequency, f & 3 & 1 & 6 & 4 & 6 & 3 & 1 & 2 \\ \hline \end{tabular}
The mean is □\square (Round to 3 decimal places as needed.)

Studdy Solution

STEP 1

1. The scores x x are 1,2,3,4,5,6,7,8 1, 2, 3, 4, 5, 6, 7, 8 .
2. The corresponding frequencies f f are 3,1,6,4,6,3,1,2 3, 1, 6, 4, 6, 3, 1, 2 .
3. The mean is calculated as the sum of the products of scores and their frequencies divided by the total number of observations.

STEP 2

1. Calculate the sum of the products of each score and its frequency.
2. Calculate the total number of observations.
3. Divide the sum from step 1 by the total from step 2 to find the mean.

STEP 3

Calculate the products of each score and its frequency:
\begin{align*} 1 \times 3 &= 3, \\ 2 \times 1 &= 2, \\ 3 \times 6 &= 18, \\ 4 \times 4 &= 16, \\ 5 \times 6 &= 30, \\ 6 \times 3 &= 18, \\ 7 \times 1 &= 7, \\ 8 \times 2 &= 16. \end{align*}

STEP 4

Sum the products:
3+2+18+16+30+18+7+16=1103 + 2 + 18 + 16 + 30 + 18 + 7 + 16 = 110

STEP 5

Calculate the total number of observations by summing the frequencies:
3+1+6+4+6+3+1+2=263 + 1 + 6 + 4 + 6 + 3 + 1 + 2 = 26

STEP 6

Divide the sum of the products by the total number of observations to find the mean:
Mean=11026≈4.231\text{Mean} = \frac{110}{26} \approx 4.231
The mean is:
4.231 \boxed{4.231}

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