The director of a local summer camp is interested in the number of hours kids spend on screens each week. He surveys a group of 15 kids at his camp and asks them how many hours they spent on screens last week. A list of his results follows.

Question

{0,7,8,8,10,11,14,15,17,17.5,18,18,18,20,30}

The director realizes he forgot to include the data value “15” in his dataset. Calculate the interquartile range of the original dataset and the interquartile range of the new dataset after “15” is added.

(1 point)
The interquartile range of the original dataset is hours.

The interquartile range of the new dataset after “15" is added is hours.

Answer 1

To calculate the interquartile range of the original dataset, we first need to find the lower quartile (Q1) and upper quartile (Q3).

First, arrange the original dataset in numerical order:
{0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 18, 20, 30}

Q1 = 8
Q3 = 18

Interquartile range = Q3 - Q1 = 18 - 8 = 10

Therefore, the interquartile range of the original dataset is 10 hours.

To calculate the interquartile range of the new dataset after "15" is added, we need to include the value 15 in the dataset and then recalculate Q1 and Q3:

{0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}

Q1 = 9
Q3 = 18

Interquartile range = Q3 - Q1 = 18 - 9 = 9

Therefore, the interquartile range of the new dataset after "15" is added is 9 hours.