The mean score of 9 students in a mathematics test was calculated as 12. It was later disc… — JAMB UTME

The mean score of $9$ students in a mathematics test was calculated as $12$ . It was later discovered that a score of $5$ was incorrectly recorded as $14$ , and an additional student's score of $31$ was omitted entirely. What is the correct mean score of all $10$ students?

$13$ Answer
B
$13.9$
C
$14.4$
D
$14.8$

Answer

The correct mean score of all 10 students is

13

The original sum of

9

scores is

108

. Subtracting the incorrect value (

14

) and adding the true value (

5

) reduces the sum of the

9

scores to

99

. Adding the

10^{\text{th}}

score of

31

gives a total sum of

130

. Dividing

130

10

gives the correct mean of

13

Step-by-Step Solution

Calculate the initial total sum of the original 9 scores.

Initial sum

= 9 \times 12 = 108

Mean is defined as total sum divided by number of items, so total sum equals mean times count.

Adjust the total sum for the misread score.

Corrected sum of 9 scores

= 108 - 14 + 5 = 99

Subtract the incorrect value (

14

) and add the actual value (

5

Add the omitted 10th score to the sum.

New total sum

= 99 + 31 = 130

Including the omitted score increases the total score sum.

Divide the new total sum by the updated total number of students.

Correct mean

= \frac{130}{10} = 13

The total number of students increased from 9 to 10.

Key Concept

Correcting the mean of ungrouped data after data entry errors or additions

Estimated Time:1m 30s

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