A data set includes the following grades: 98, 94, 93, 82, 61, 80. Suppose that 61 is removed from the data. How is the median affected?

Question

Responses

A The median increases by 5.The median increases by 5.

B The median increases by 5.5.The median increases by 5.5.

C The median decreases by 1.The median decreases by 1.

D The median does not change

Answer 1

To find out how the median is affected when the lowest grade (61) is removed, let's first calculate the median of the original data set and then the median after removing 61.

Original set of grades: 98, 94, 93, 82, 61, 80

1. Sort the grades: 61, 80, 82, 93, 94, 98

2. The number of grades is 6 (an even number). The median is found by taking the average of the two middle numbers. The two middle numbers are 82 and 93.

   Median = (82 + 93) / 2 = 175 / 2 = 87.5

New set of grades after removing 61: 98, 94, 93, 82, 80

1. Sort the grades: 80, 82, 93, 94, 98
2. Now, the number of grades is 5 (an odd number). The median is the middle number. The middle number (3rd grade) is 93.

Now, we can compare the medians:

• Original median: 87.5
• New median after removing 61: 93

Thus, the median increases by:

93 - 87.5 = 5.5

So, the correct response is B: The median increases by 5.5.