Question

Given the following box plot:

Figure 2.41

a. which quarter has the smallest spread of data? What is that spread?

b. which quarter has the largest spread of data? What is that spread?

c. find the interquartile range (IQR).

d. are there more data in the interval 5–10 or in the interval 10–13? How do you know this?

e. which interval has the fewest data in it? How do you know this?

i. 0–2

ii. 2–4

iii. 10–12

iv. 12–13

v. need more information

Short answer

a) The last$25\%$spread (Q3 to max) was between 12 and 13.

b) The second is a $25\%$spread (Q 1-Q 2), with a range of 2-10.

c) $IQR=Q_3-Q_1=12-2=10$

d) In the range 10-13, there is more information. This interval contains 50% of the data distribution. Since the interval 2-10 contains just 25%, the interval 5-10 will contain less than 25%.

e) Even though it is less than 25%, the interval 2-4 has the smallest proportion of data; it is a subset of the interval 2-10. The data is held in all of the other intervals by a 25%.

Step-by-step solution

Explanation for the solution

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is rightskewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

We are given the below box plot:

Part (a) - Step 2: To find

Which quarter has the smallest spread of data? What is the spread?

Part(a) - Step 3: Solution

Consider the above box plot:

a) The last 25% spread (Q3 to max) was between 12 and 13.

Part (b) - Step 4: To find

Which quarter has the largest spread of data? What is the spread?

Part(b) - Step 5: Solution

Consider the above box plot:

b) The second is a 25% spread (Q 1-Q 2), with a range of 2-10.

Part (c) - Step 6: To find

Find the interquartile range?

Part (c) - Step 7: Solution

Consider the above box plot:

c) $IQR=Q_3-Q_1=12-2=10$

Part(d) - Step 8: To find

Are there more data in the interval 5-10 or in the interval 10-13? How do you know?

Part (d) - Step 9: Solution

In the range 10-13, there is more information. This interval contains 50% of the data distribution. Since the interval 2-10 contains just 25%, the interval 5-10 will contain less than 25%.

Part (e) - Step 10: To find

Which interval has the fewest data in it?

Part(e) - Step 11: Solutrion

Even though it is less than 25%, the interval 2-4 has the smallest proportion of data; it is a subset of the interval 2-10. The data is held in all of the other intervals by a 25%.