Question

the test scores for last weeks history test were: 76, 100, 94, 90, 68, 90, 80, 92, 84. if test scores of 60 and 68 are added to the list, what would happen to the mean and median? a the mean and median stay the same. b the mean and the median become equal. c the mean and median get closer together. d the mean and the median get further apart

Explanation:

Step1: Calculate initial mean

The sum of the original scores \(76 + 100+94 + 90+68+90+80+92+84=784\), and there are \(n = 9\) scores. The original mean \(\bar{x}_1=\frac{784}{9}\approx87.11\).

Step2: Calculate initial median

Arrange the original scores in ascending - order: \(68,76,80,84,90,90,92,94,100\). The median \(M_1 = 90\) (the 5th value when \(n = 9\)).

Step3: Calculate new mean

Add \(60\) and \(68\) to the data - set. The new sum is \(784+60 + 68=912\), and the new number of scores is \(n_2=9 + 2=11\). The new mean \(\bar{x}_2=\frac{912}{11}\approx82.91\).

Step4: Calculate new median

Arrange the new scores in ascending - order: \(60,68,68,76,80,84,90,90,92,94,100\). The median \(M_2 = 84\) (the 6th value when \(n = 11\)).

Step5: Analyze the change

The original mean was approximately \(87.11\) and the new mean is approximately \(82.91\), the original median was \(90\) and the new median is \(84\). The difference between the mean and median has increased, so they get further apart.

Answer:

D. The mean and the median get further apart