Mathematics : asked on bm42400

23.04.2023

Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions. Two box plots shown. The top one is labeled Males. Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30. The bottom box plot is labeled Females. Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum shown

Part A: Estimate the IQR for the males' data. (2 points)

Part B: Estimate the difference between the median values of each data set. (2 points)

Part C: Describe the distribution of the data and if the mean or median would be a better measure of center for each. (4 points)

Part D: Provide a possible reason for the outlier in the data set. (2 points)

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17.02.2022, solved by verified expert

Bibin (Bibi) P B

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(A) The IQR for the males' data is 11.

(B) The difference between the median values of each data set = 18 - 10.5 = 7.5.

(C) The distribution of the males' data is an asymmetrical distribution or we can say the right-skewed distribution and the median would be a better measure of the center.

The distribution of the females' data is a symmetrical distribution or we can say the normal distribution and the mean would be a better measure of the center.

(D) In the males' data, we see that there is only one outlier at a value of 30.

Step-by-step explanation:

We are given the following information about the two box plots of male and female below;

The top one is labeled Males: Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30.

The bottom box plot is labeled as Females: Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum is shown.

(A) The Interquartile range (IQR) is the difference between the third quartile and the first quartile of the data set.

In a box plot representing the males;

= 14 and = 3

So, IQR = - = 14 - 3 = 11.

Hence, the IQR for the males' data is 11.

(B) The median value of the males' data is given as 10.5 and the median value of the females' data is given as 18.

So, the difference between the median values of each data set = 18 - 10.5 = 7.5.

(C) The distribution of the males' data is an asymmetrical distribution or we can say the right-skewed distribution because the values after the third quartile are very far and also the lower quartile range is much larger than the upper quartile range. Also, there is one outlier in males' data also.

So, for any asymmetrical distribution, the median would be a better measure of the center as it does not take into account the outliers' value and gives the middlemost data value.

The distribution of the females' data is a symmetrical distribution or we can say the normal distribution because the data values are equally spread and the median is at the center of the two quartile values.

So, for any symmetrical distribution, although the mean and median are the same; the mean would be a better measure of the center as it does take into account all the data values and gives the average of the data set.

(D) Yes, there is one outlier in the males' data set. Outliers are those values that fall very far from all other values.

In a box plot data, outliers are represented as single points outside the whiskers.

In the males' data, we see that there is only one outlier at a value of 30. This represents a case in which a male attended the movie theater on the 30th day of the month. This is an invalid case since the maximum of the male plot is at 21, which means that no males attended the movie after the 21st.

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Mathematics

Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions. Two box plots shown. The top one is labeled Males. Minimum at 0, Q1 at 1, median at 20, Q3 at 25, maximum at 50. The bottom box plot is labeled Females. Minimum at 0, Q1 at 5, median at 6, Q3 at 10, maximum at 18 and a point at 43 Part A: Estimate the IQR for the males data. (2 points) Part B: Estimate the difference between the median values of each data set. (2 points) Part C: Describe the distribution

Step-by-step answer

P Answered by Specialist

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Mathematics

Use the box plots comparing the number of males and number of females attending the latest superhero movie each day for a month to answer the questions. Two box plots shown. The top one is labeled Males. Minimum at 1, Q1 at 3, median at 10.5, Q3 at 14, maximum at 21, and a point at 30. The bottom box plot is labeled Females. Minimum at 0, Q1 at 15, median at 18, Q3 at 21, no maximum shown Part A: Estimate the IQR for the males data. (2 points) Part B: Estimate the difference between the median values of each data set. (2 points) Part C: Describe

Step-by-step answer

P Answered by Specialist

Hey There!!

The answer to this is: A) Interquartile range - For males: 11, for femals: 6

B) Difference between the median values: 7.5

C) Males: median, females: mean

D) Outlier: one male attended the move on the 30th A) The interquartile range (IQR) of a set of data is the difference between the upper quartile (Q3) and the lower quartile (Q1):

IQR = Q3 - Q1

- For the box plot representing males:

Lower quartile is Q1=3

Upper quartile is Q3 = 14

Therefore, interquartile range is

IQR = 14 - 3 = 11

- For the box plot representing females:

Lower quartile is Q1 = 15

Upper quartile is Q3 = 21

Therefore, interquartile range is

IQR = 21 - 15 = 6

B) The median value of a dataset is the "central value" of the dataset, i.e. the value of the dataset for which half of the values in the dataset are lower than the median, and half of the values in the dataset are higher than the median.

The median value of a dataset is indicated as Q2.

Here the median values for the two datasets are given:

- For males, Q2 = 10.5

- For females, Q2 = 18

Therefore, the difference between the median values is

Delta Q2 = 18-10.5 = 7.5

C) The mean of a dataset is the average value of the dataset, calculated as the sum of all data divided by the number of values in the dataset.

On the other hand, the median of a dataset is the central value, i.e. the value for which half of the values in the dataset are lower than the median, and half of the values in the dataset are higher than the median.

For a perfectly symmetrical distribution, mean and median are equal; however, for non-symmetrical distribution, this is not true.

In general, the mean is a good to describe a distribution when the distribution itself is symmetrical; instead, when the distribution is very asymmetrical, the median provides a better indicator for the distribution.

In this case, we can see that the male distribution is very asymmetrical: in fact, the lower quartile range (Q2 - Q1) is much larger than the upper quartile range (Q3 - Q2) , so the distribution can be better describes using the median. For the female case instead, the distribution is more symmetrical (the median is at the center between Q_1 and Q_3), therefore the distribution can be better described by using the mean.

4) An outlier of a dataset is a value of the dataset that falls very far from all other values.

In a box plot, outliers are represented as single points outside the whiskers.

In this case, we see that there is only one outlier, in the male plot, at a value of 30. This represents a single case in which a male attended the movie theater on the 30th. This is an isolated case, since the maximum of the male plot is at 21, which means that no males attended the movie after the 21st.

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