Question

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

Explanation:

Step1: Calculate total students

Sum all frequencies:
$2 + 1 + 0 + 2 + 3 + 3 + 2 + 3 = 16$

Step2: Compute total score points

Multiply score by frequency, sum:
$(3×2)+(4×1)+(5×0)+(6×2)+(7×3)+(8×3)+(9×2)+(10×3)$
$=6 + 4 + 0 + 12 + 21 + 24 + 18 + 30 = 115$

Step3: Find the mean score

Divide total points by total students:
$\text{Mean} = \frac{115}{16} = 7.3125 ≈ 7.3$

Step4: Locate median position

For $n=16$, median is average of 8th and 9th values.

Step5: Identify ordered score positions

Cumulative frequencies:
3 (2), 4 (3), 6 (5), 7 (8), 8 (11), 9 (13), 10 (16)
8th value = 7, 9th value = 8

Step6: Calculate median

Average the two middle values:
$\text{Median} = \frac{7+8}{2} = 7.5$
Wait, correction: Cumulative frequency check:
1-2: 3, 3:4, 4-5:6, 6-8:7, 9-11:8, 12-13:9, 14-16:10
8th value is 7, 9th value is 8. Median = $\frac{7+8}{2}=7.5$? No, wait cumulative frequency:
After 3: 2 students (positions 1-2)
After 4: 3 students (position 3)
After 6: 5 students (positions 4-5)
After 7: 8 students (positions 6-8)
After 8: 11 students (positions 9-11)
Ah, 8th position is 7, 9th position is 8. So median is $\frac{7+8}{2}=7.5$. But often rounded or exact: 7.5. But let's confirm:
Total students 16, even number, median is average of 8th and 9th term.
Ordered scores: [3,3,4,6,6,7,7,7,8,8,8,9,9,10,10,10]
8th term:7, 9th term:8. Median = $\frac{7+8}{2}=7.5$

Final correction:

Step1: Total students count

Sum frequencies: $2+1+0+2+3+3+2+3=16$

Step2: Total score sum

$\sum(\text{Score}×\text{Frequency})=115$

Step3: Compute mean

$\text{Mean}=\frac{115}{16}=7.3125$

Step4: List ordered scores

[3,3,4,6,6,7,7,7,8,8,8,9,9,10,10,10]

Step5: Find median (8th+9th)/2

$\text{Median}=\frac{7+8}{2}=7.5$

Answer:

Mean = 7.3, Median = 8