Question

the table below shows the scores of a group of students on a 10-point quiz.
test score frequency
3 3
4 3
5 1
6 1
7 2
8 0
9 3
10 3
the mean score on this test is:
the median score on this test is:
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Explanation:

Step1: Calculate total students

$3+3+1+1+2+0+3+3=16$

Step2: Calculate total score sum

$(3×3)+(4×3)+(5×1)+(6×1)+(7×2)+(8×0)+(9×3)+(10×3)$
$=9+12+5+6+14+0+27+30=103$

Step3: Compute mean score

$\text{Mean}=\frac{\text{Total Score}}{\text{Total Students}}=\frac{103}{16}=6.4375$

Step4: Locate median position

$\text{Median position}=\frac{16}{2}=8$ and $\frac{16}{2}+1=9$. We need the average of the 8th and 9th values.

Step5: List ordered scores to find 8th/9th values

Ordered scores: 3,3,3,4,4,4,5,6,7,7,9,9,9,10,10,10
8th value = 6, 9th value =7

Step6: Compute median score

$\text{Median}=\frac{6+7}{2}=6.5$

Answer:

The mean score on this test is: $6.4375$
The median score on this test is: $6.5$