Question

1. robin collected data on the number of hours she watched television on sunday through thursday nights for a period of 3 weeks. the data are shown in the table below. using an appropriate scale on the number line below, construct a box plot for the 15 values. 5. the data set 20, 36, 52, 56, 24, 16, 40, 4, 28 represents the number of books purchased by nine book club members in a year. construct a box plot for these data on the number line below. 6. what is the value of the third quartile in the box plot shown below? 1) 18 2) 22 3) 36 4) 46

Explanation:

Question 4:

Step 1: List all data points

First, we extract the data from the table. For Week 1: 4, 3, 2.5, 2, 2; Week 2: 4.5, 3, 2.5, 3, 1.5; Week 3: 4, 3, 1, 1.5, 2.5. Combining all these, we have the 15 data points: 4, 3, 2.5, 2, 2, 4.5, 3, 2.5, 3, 1.5, 4, 3, 1, 1.5, 2.5.

Step 2: Sort the data

Sorting the data in ascending order: 1, 1.5, 1.5, 2, 2, 2.5, 2.5, 2.5, 3, 3, 3, 3, 4, 4, 4.5.

Step 3: Find the median (Q2)

Since there are 15 data points (odd number), the median is the 8th value. The 8th value is 2.5.

Step 4: Find Q1 (median of lower half)

The lower half of the data (excluding the median) has 7 values: 1, 1.5, 1.5, 2, 2, 2.5, 2.5. The median of this lower half is the 4th value, which is 2.

Step 5: Find Q3 (median of upper half)

The upper half of the data (excluding the median) has 7 values: 3, 3, 3, 3, 4, 4, 4.5. The median of this upper half is the 4th value, which is 3.

Step 6: Identify the minimum and maximum

The minimum value is 1, and the maximum value is 4.5.

Step 7: Construct the box plot

• Draw a number line that includes the range from 1 to 4.5.
• Plot the minimum (1), Q1 (2), median (2.5), Q3 (3), and maximum (4.5).
• Draw a box from Q1 to Q3, with a line inside the box at the median.
• Draw whiskers from the box to the minimum and maximum values.

Question 5:

Step 1: List the data set

The data set is: 20, 36, 52, 56, 24, 16, 40, 4, 28.

Step 2: Sort the data

Sorting the data in ascending order: 4, 16, 20, 24, 28, 36, 40, 52, 56.

Step 3: Find the median (Q2)

Since there are 9 data points (odd number), the median is the 5th value. The 5th value is 28.

Step 4: Find Q1 (median of lower half)

The lower half of the data (excluding the median) has 4 values: 4, 16, 20, 24. The median of this lower half is the average of the 2nd and 3rd values: $\frac{16 + 20}{2} = 18$.

Step 5: Find Q3 (median of upper half)

The upper half of the data (excluding the median) has 4 values: 36, 40, 52, 56. The median of this upper half is the average of the 2nd and 3rd values: $\frac{40 + 52}{2} = 46$. Wait, no, wait. Wait, the upper half is 36, 40, 52, 56? Wait, no, the data after the median (28) is 36, 40, 52, 56? Wait, no, the sorted data is 4, 16, 20, 24, 28, 36, 40, 52, 56. So the upper half is the values above the median: 36, 40, 52, 56. Wait, no, the median is the 5th value (28), so the lower half is the first 4 values: 4, 16, 20, 24. The upper half is the last 4 values: 36, 40, 52, 56. Wait, but to find Q3, we take the median of the upper half. The upper half has 4 values, so the median is the average of the 2nd and 3rd values in the upper half. The upper half sorted is 36, 40, 52, 56. So the 2nd value is 40, the 3rd is 52. So Q3 is $\frac{40 + 52}{2} = 46$? Wait, but let's check again. Wait, maybe I made a mistake. Wait, the data set is 9 values. So the median is the 5th value: 28. Then the lower half is the first 4 values: 4, 16, 20, 24. The median of the lower half is (16 + 20)/2 = 18 (Q1). The upper half is the last 4 values: 36, 40, 52, 56. The median of the upper half is (40 + 52)/2 = 46 (Q3). The minimum is 4, maximum is 56.

Step 6: Construct the box plot

• Draw a number line from 0 to 60 (as given).
• Plot the minimum (4), Q1 (18), median (28), Q3 (46), and maximum (56).
• Draw a box from Q1 to Q3, with a line inside the box at the median.
• Draw whiskers from the box to the minimum and maximum values.

Question 6:

Step 1: Recall the box plot components

In a box plot, the box represents the interquartile range (IQR), with the left end of the box being the first quartile (Q1) and the right end of the box being the third quartile (Q3).

Step 2: Identify the right end of the box

Looking at the given box plot, the right end of the box is at 36 on the number line.

Answer:

s:

Question 4:

The box plot is constructed with minimum = 1, Q1 = 2, median = 2.5, Q3 = 3, maximum = 4.5. (Note: Since the problem asks to construct the box plot, the final answer here is the constructed box plot as per the steps above.)

Question 5:

The box plot is constructed with minimum = 4, Q1 = 18, median = 28, Q3 = 46, maximum = 56. (Note: Since the problem asks to construct the box plot, the final answer here is the constructed box plot as per the steps above.)

Question 6: