Question

The mean and median scores of a recent Stat 111 exam were close to 68%. The instructor decided not to count one score of zero that was from an absent student to get a better representation of the class average and then recalculated the new mean and median.

a) Will the new mean increase, decrease or remain about the same? Explain.
b) Will the new median increase, decrease or remain about the same? Explain.
c) Will the overall range increase, decrease or remain about the same? Explain.
d) Will the IQR increase, decrease or remain about the same? Explain.
The mean and median"

Answer 1

The new mean will increase, the new median will remain about the same, the overall range will decrease, and the IQR will remain about the same after removing an outlier with a score of zero.

Step-by-step explanation:

a) The new mean will increase. The mean is heavily influenced by outliers, and in this case, the score of zero is an outlier since it is much lower than the other scores. By removing this outlier, the overall mean will increase.

b) The new median will remain about the same. The median is not affected by outliers, so removing the score of zero will not have an impact on the median.

c) The overall range will decrease. The range is the difference between the highest and lowest scores. By removing the score of zero, which is a very low score, the overall range will be smaller.

d) The IQR will remain about the same. The IQR is a measure of the spread of the middle 50% of the data, and it is not affected by outliers. Therefore, removing the score of zero will not have an impact on the IQR.