Question

The following table shows the number of hours some high school students in 2 cities spend watching television each week: City A 21 23 24 22 24 25 23 23 22 City B 24 22 20 23 23 50 20 46 21 Create a five-number summary and calculate the interquartile range for the two sets of data.

Answer 1

24.5

Explanation:

To create a five-number summary for each set of data (City A and City B) and calculate the interquartile range (IQR), you need to find the following statistics:

1. Minimum (Min): The smallest value in the data.

2. Q1 (First Quartile): The 25th percentile, separating the lowest 25% of the data.

3. Median (Q2): The middle value when the data is sorted.

4. Q3 (Third Quartile): The 75th percentile, separating the lowest 75% of the data.

5. Maximum (Max): The largest value in the data.

Let's first calculate these statistics for both City A and City B's data:

For City A:

Sorted data: 21, 22, 22, 23, 23, 23, 24, 24, 25

Min = 21

Q1 = 22

Median (Q2) = 23

Q3 = 24

Max = 25

For City B:

Sorted data: 20, 20, 21, 22, 23, 23, 23, 24, 46, 50

Min = 20

Q1 = 21.5 (average of the 5th and 6th values)

Median (Q2) = 23

Q3 = 46 (The outlier at 50 doesn't affect Q3 since it's larger)

Max = 50

Now, calculate the interquartile range (IQR) for each city:

For City A:

IQR = Q3 - Q1 = 24 - 22 = 2

For City B:

IQR = Q3 - Q1 = 46 - 21.5 = 24.5

So, the five-number summary and IQR for City A are:

Min = 21

Q1 = 22

Median (Q2) = 23

Q3 = 24

Max = 25

IQR = 2

For City B:

Min = 20

Q1 = 21.5

Median (Q2) = 23

Q3 = 46

Max = 50

IQR = 24.5

Hope this helps