Question

use this data set for 3 and 4.
7, 13, 9, 15, 11, 7, 11

1. find the interquartile range.

a 11 c 7
b 6 d 13

1. which is the correct box-and-whisker plot for the data set?

a box - and - whisker plot a
b box - and - whisker plot b
c box - and - whisker plot c
d box - and - whisker plot d

Explanation:

Question 3

Step1: Order the data set

First, we order the data set \( 7, 13, 9, 15, 11, 7, 11 \) from least to greatest.
So, the ordered data set is \( 7, 7, 9, 11, 11, 13, 15 \).

Step2: Find the median (Q2)

The number of data points \( n = 7 \), which is odd. The median (Q2) is the middle value, which is the \( \frac{n + 1}{2} = \frac{7 + 1}{2} = 4 \)-th value.
Looking at the ordered data set \( 7, 7, 9, 11, 11, 13, 15 \), the 4th value is \( 11 \). So, \( \text{Q2} = 11 \).

Step3: Find Q1 (median of lower half)

The lower half of the data set (excluding the median) is \( 7, 7, 9 \). The number of values in the lower half is \( 3 \) (odd). The median of the lower half (Q1) is the middle value, which is the \( \frac{3 + 1}{2} = 2 \)-nd value.
For \( 7, 7, 9 \), the 2nd value is \( 7 \). So, \( \text{Q1} = 7 \).

Step4: Find Q3 (median of upper half)

The upper half of the data set (excluding the median) is \( 11, 13, 15 \). The number of values in the upper half is \( 3 \) (odd). The median of the upper half (Q3) is the middle value, which is the \( \frac{3 + 1}{2} = 2 \)-nd value.
For \( 11, 13, 15 \), the 2nd value is \( 13 \). So, \( \text{Q3} = 13 \).

Step5: Calculate the interquartile range (IQR)

The interquartile range is calculated as \( \text{IQR} = \text{Q3} - \text{Q1} \).
Substituting the values of Q3 and Q1, we get \( \text{IQR} = 13 - 7 = 6 \).

To determine the correct box - and - whisker plot, we first find the minimum, Q1, median (Q2), Q3, and maximum values from the data set \( 7, 7, 9, 11, 11, 13, 15 \):

• Minimum value: \( 7 \)
• Q1: \( 7 \) (calculated in question 3)
• Median (Q2): \( 11 \) (calculated in question 3)
• Q3: \( 13 \) (calculated in question 3)
• Maximum value: \( 15 \)

Now let's analyze each option:

• Option A: Check the positions of min, Q1, median, Q3, max. The minimum here does not match \( 7 \), so A is incorrect.
• Option B: The minimum value is \( 7 \), Q1 is \( 7 \), median is \( 11 \), Q3 is \( 13 \), and maximum is \( 15 \). All these values match our calculated values for the box - and - whisker plot parameters.
• Option C: The Q1 and median values do not match our calculations, so C is incorrect.
• Option D: The Q1, median, Q3 and min/max values do not match our calculations, so D is incorrect.

Answer:

B 6

Question 4