Question

The average high temperatures in degrees for a city are listed.

58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

If a value of 60° is added to the data, how does the median change?

The median stays at 80°.
The median stays at 79.5°.
The median decreases to 77°.
The median decreases to 82°.

Answer 1

To determine how the median changes when a value of 60° is added to the data, let's calculate the median before and after the addition.

Original data:
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57

The median is the middle value when the data is arranged in ascending order. In this case, the median is between the two middle values since there are an even number of values.

Arranging the data in ascending order:
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

The median is the average of the two middle values: 77 and 82.
Median = (77 + 82) / 2 = 79.5°

Now, let's add the value of 60° to the data:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105, 60

Arranging the updated data in ascending order:
57, 58, 60, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105

The median is now the middle value, which is 77.

Therefore, the median decreases to 77° when a value of 60° is added to the data.
The correct option is: "The median decreases to 77°."