Question

The following table shows the number of hours some students in two neighborhoods spend on social media each day:

Neighborhood A

5

2

4

2

5

5

4

5

2

Neighborhood B

4

5

5

1

12

2

2

1

3



Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (5 points)
Part B: Are there any outliers present for either data set? Justify your answer mathematically. (5 points)

Answer 1

The five-number summary for the two sets of data is calculated, and the interquartile range (IQR) is determined. Additionally, it is found that there is an outlier present in the data set for Neighborhood B.

Step-by-step explanation:

Part A: To find the five-number summary for each set of data, we need to find the minimum value, Q1, Q2 (median), Q3, and maximum value. For Neighborhood A, the five-number summary is:

• Minimum: 2
• Q1: 2
• Median (Q2): 4.5
• Q3: 5
• Maximum: 5

For Neighborhood B, the five-number summary is:

• Minimum: 1
• Q1: 2
• Median (Q2): 4
• Q3: 5
• Maximum: 12

To calculate the interquartile range (IQR), subtract Q1 from Q3. For Neighborhood A, IQR = 5 - 2 = 3. For Neighborhood B, IQR = 5 - 2 = 3.

Part B: To determine if there are any outliers, we can use the rule that considers a data point to be an outlier if it is less than Q1 - 1.5 * IQR or greater than Q3 + 1.5 * IQR.

For Neighborhood A, there are no outliers. For Neighborhood B, the value 12 is greater than Q3 + 1.5 * IQR (5 + 1.5 * 3) = 9.5, so it is considered an outlier.