Mathematics : asked on carts66
 31.03.2021

These box plots show daily low temperatures for a sample of days in two different towns.


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Step-by-step answer

24.06.2022, solved by verified expert
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Answer: B. The interquartile range (IQR) for town A, 20", is greater than the IQR for town B, 10'.

Explanation:
IQR=Q₃-Q₁.

For the town A:

Q₃=40 and Q₁=20.

IQR of town A=40-20=20.
For the town B:

Q₃=30  and Q₁=20.

IQR of town A=30-20=10.
The most statement is appropriate comparison of the spreads is B (The interquartile range (IQR) for town A, 20, is greater than the IQR for town B, 10).



 

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Faq

Mathematics
Step-by-step answer
P Answered by PhD

C. The distribution for town A is symmetric, but the distribution for

town B is negatively skewed.

Step-by-step Explanation:

From the box plots attached in the diagram below, which shows data of low temperatures for town A and town B for some days, we can compare the shapes of the box plot by visually analysing both box plots and how the data for each town is distributed.

=> For town A, the shape of the box plot is symmetric because both quartiles seem equal, and the median also divides the rectangular box into two equal halves. Both whiskers also appear to be of equal lengths.

The box plot for Town A takes a symmetric shape, and this shows a typical normal distribution of data.

=> On the other hand, Town B data distribution is different. The median seem close to the top half of the box and does not divide the box into equal halves. This shows the distribution is skewed. Since the whisker is shorter from the upper end of the box to the left side, we can infer that the distribution for Town B is skewed to the left, and it is negatively skewed.

=> The right comparison of the shapes of the box plots is "C. The distribution for town A is symmetric, but the distribution for town B is negatively skewed."


These box plots show daily low temperatures for a sample of days in two

different towns
Town A
15
2
Mathematics
Step-by-step answer
P Answered by PhD

C. The distribution for town A is symmetric, but the distribution for

town B is negatively skewed.

Step-by-step Explanation:

From the box plots attached in the diagram below, which shows data of low temperatures for town A and town B for some days, we can compare the shapes of the box plot by visually analysing both box plots and how the data for each town is distributed.

=> For town A, the shape of the box plot is symmetric because both quartiles seem equal, and the median also divides the rectangular box into two equal halves. Both whiskers also appear to be of equal lengths.

The box plot for Town A takes a symmetric shape, and this shows a typical normal distribution of data.

=> On the other hand, Town B data distribution is different. The median seem close to the top half of the box and does not divide the box into equal halves. This shows the distribution is skewed. Since the whisker is shorter from the upper end of the box to the left side, we can infer that the distribution for Town B is skewed to the left, and it is negatively skewed.

=> The right comparison of the shapes of the box plots is "C. The distribution for town A is symmetric, but the distribution for town B is negatively skewed."


These box plots show daily low temperatures for a sample of days in two

different towns
Town A
15
2
Mathematics
Step-by-step answer
P Answered by PhD

*The question is incomplete. Attached below is the diagram of the box plots being referred to followed by the complete question and options.

D. The median for town A, 20 degrees, is less than the median of town B, 30 degrees

Step-by-step Explanation:

From the given diagram of the box plots showing the daily low temperatures for town A and B, the median of town A and B is shown on the box plots by the line that divides the box. Therefore, the median of town A is where the line that divides the box is. Median for town A is 20⁰. Same applies for town B. Town B median is 30⁰.

Therefore, option D is the most appropriate comparison of the centers. Median of town A is less than median of town B.


These box plots show daily low temperatures for a sample of days in two different towns.

Town A. 10
Mathematics
Step-by-step answer
P Answered by PhD

Given:

The box plots show daily low temperatures for a sample of days in two different towns.

We need to determine the most appropriate comparison of the spreads.

Interquartile range of town A:

The interquartile range can be determined by subtracting the end values of the boxes.

Thus, we have;

Interquartile range = 30 - 15

Interquartile range = 15

Thus, the interquartile range for town A is 15.

Interquartile range for town B:

The interquartile range for town B is given by

Interquartile range = 40 - 20

Interquartile range = 20

Thus, the interquartile range for town B is 20.

Hence, the interquartile range (IQR) for town A, 15° is less than the IQR for town B, 20°

Hence, Option A is the correct answer.

Mathematics
Step-by-step answer
P Answered by PhD

Choice A is correct

Step-by-step explanation:

The distribution for town A is symmetric, but the distribution for town B is negatively skewed. From the box plots it is clear that the tails of the box plot  for town A are equal in length while for town B the left tail is longer implying a negatively skewed distribution.

Mathematics
Step-by-step answer
P Answered by PhD
Choice A.

The distribution for town A is positively skewed, but the distribution for town B is symmetric.

Explanation:

The length of the whiskers tell us if we're dealing with a symmetric distribution, or a skewed distribution. For town A, the right whisker is longer than the left whisker. So this distribution is positively skewed. We can say it is skewed to the right, or right skewed.

Town B has whiskers of equal length. In addition, the two distances inside the box are equal to one another. We have a perfectly symmetric distribution. One half is a mirror copy of the other half.

Mathematics
Step-by-step answer
P Answered by Specialist

B) The median for Town A, 30, is less than the median of town B, 40.

Explanation:

In a box plot, the line in the center of the box represents the median.  The box plot for town A has a line in the middle at 30; this is its median.

The box plot for town B has a line in the middle at 40; this is its median.

The median for town A is less than the median for town B.

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