Question

how would the data be affected if the lowest quiz score was dropped from the data listed below? 72, 89, 99, 80, 55 the mean would decrease by 2 points the mean would increase by 6 points the median would decrease by 5 points the median would increase 10 points

Explanation:

Step1: Identify lowest score

The lowest score in {72, 89, 99, 80, 55} is 55.

Step2: Calculate original mean

Sum original scores: $72 + 89 + 99 + 80 + 55 = 395$
Mean: $\frac{395}{5} = 79$

Step3: Calculate new mean (drop 55)

Sum new scores: $395 - 55 = 340$
Mean: $\frac{340}{4} = 85$

Step4: Compare means

Difference: $85 - 79 = 6$

Step5: Calculate original median

Sort original scores: {55, 72, 80, 89, 99}
Median (3rd value): $80$

Step6: Calculate new median

Sort new scores: {72, 80, 89, 99}
Median (avg of 2nd/3rd): $\frac{80+89}{2} = 84.5$
Median change is not an option, so focus on mean.

Answer:

B. The mean would increase by 6 points