Question

When the scores for a recent Chemistry exam were calculated, the mean was 60 and the median was 65. Later the professor discovered that one score had been recorded incorrectly; it had been entered into the computer as a 5, instead of as a 50. When this correction is made, _________.

Answer 1

The correction of a mistaken exam score from 5 to 50 will result in an increase in the mean score. The median may or may not change depending on whether the corrected score affects the middle of the ordered data set.

Step-by-step explanation:

When the incorrect score of 5 on a Chemistry exam is corrected to 50, both the mean and the median of the exam scores will be affected. Because the mean is sensitive to the exact values of all scores in the data set, the correction will raise the mean from 60. This is because the total sum of all the exam scores will increase by 45 (the difference between the incorrect score and the correct score), which will then be divided amongst the number of students to find the new mean.

The change in the median depends on the position of the incorrectly recorded score relative to the other scores. If the incorrectly recorded score of 5 was changing the order of the data set, its correction might also change the median. However, if the corrected score of 50 still falls below the median score of 65, then the median might remain unchanged. Median is the middle value of an ordered set of data, so unless the correction displaces the middle score(s), the median will stay the same.

Answer 2

Mean of the exam scores will change but median will remain the same.

Step-by-step explanation:

To solve this question we have to understand the difference in mean and median of any set of data.

Mean is simply an arithmetic mean of the data.

If the set of data is 1, 2, 3, 4, 5, 6, 7

Then mean of this data =
`\frac{\text{Total of data}}{\text{Numbers of data given in the set}}`

=
`(1+2+3+4+5+6+7)/(7)`

=
`(28)/(7)`

= 4

Median is the middle term which separates higher half of the sample from the lower half.

So median of the given data set = 4

Which is at the center.

Now the mean of the Chemistry score is 60 which will definitely change if any number in the total of the data set changes.

Which means average will change with the change of a number in the set.

But Middle term or median of the set will never change unless we add a new number in the set.

Therefore, answer will be "mean of the exam scores will change but median will remain the same."