Question

he 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.

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, let's calculate the interquartile range (IQR) of the original dataset:

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

Step 1: Find the median
Since there are 15 data points, the median is the average of the 8th and 9th values.
Median = (15 + 17) / 2 = 16

Step 2: Find Q1 (the median of the lower half of the data)
There are 7 data points below the median, so Q1 is the average of the 4th and 5th values.
Q1 = (8 + 8) / 2 = 8

Step 3: Find Q3 (the median of the upper half of the data)
There are 7 data points above the median, so Q3 is the average of the 12th and 13th values.
Q3 = (18 + 18) / 2 = 18

Step 4: Calculate IQR
IQR = Q3 - Q1 = 18-8 = 10

Now let's calculate the interquartile range of the dataset after adding “15”:

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

Step 1: Find the median
Since there are 16 data points, the median is the average of the 8th and 9th values.
Median = (15 + 17) / 2 = 16

Step 2: Find Q1 (the median of the lower half of the data)
There are 8 data points below the median, so Q1 is the average of the 4th and 5th values.
Q1 = (8 + 10) / 2 = 9

Step 3: Find Q3 (the median of the upper half of the data)
There are 8 data points above the median, so Q3 is the average of the 12th and 13th values.
Q3 = (18 + 18) / 2 = 18

Step 4: Calculate IQR
IQR = Q3 - Q1 = 18-9 = 9

Therefore, the interquartile range of the original dataset is 10, and the interquartile range of the dataset after adding “15” is 9.