Question

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. {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.
The interquartile range of the original dataset is _____ hours.
The interquartile range of the new dataset after “15" is added is ___ hours.

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

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

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

Q1 = (8 + 10) / 2 = 9
Q3 = (17 + 18) / 2 = 17.5

IQR = Q3 - Q1 = 17.5 - 9 = 8.5 hours

New dataset after adding 15:
{0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}

Sorted new dataset:
{0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}

Q1 = (8 + 10) / 2 = 9
Q3 = (17 + 18) / 2 = 17.5

IQR = Q3 - Q1 = 17.5 - 9 = 8.5 hours

Therefore, the interquartile range of the original dataset is 8.5 hours, and the interquartile range of the new dataset after "15" is added is also 8.5 hours.