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70 50 40 with quartiles Q1= 53.25, Q2= 56.0, and Q3= 70.00. BoxPlot B BoxPlot 09 06 08 ed right).

70 50 40 with quartiles Q1= 53.25, Q2= 56.0, and Q3= 70.00. BoxPlot B BoxPlot 09 06 08 ed right).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Scores on an Accounting Exam** **Overview:** Scores on an accounting exam ranged from 46 to 87, with quartiles \(Q_1 = 53.25\), \(Q_2 = 56.0\), and \(Q_3 = 70.0\). **Task:** **(a) Select the correct box plot for the given data.** - **BoxPlot A:** Displays a box with the left edge near 46 and the right edge near 56, with a longer whisker extending to the right, suggesting a positive skewness. - **BoxPlot B:** Shows a box with the left edge near 50 and the right edge near 70, with short whiskers on both sides, indicating a symmetric or slight skew. Choices: - ○ BoxPlot A - ○ BoxPlot B - ○ BoxPlot C **(b) Describe its shape (skewed left, symmetric, skewed right).** - ○ The distribution is symmetric. - ○ The distribution is skewed left. - ○ The distribution is skewed right. Boxes are graphical representations used to depict the spread of a dataset using quartiles. The box itself shows the interquartile range (IQR), while the "whiskers" extend to the minimum and maximum values within 1.5 times the IQR from the upper and lower quartiles.
Transcribed Image Text:**Scores on an Accounting Exam** **Overview:** Scores on an accounting exam ranged from 46 to 87, with quartiles \(Q_1 = 53.25\), \(Q_2 = 56.0\), and \(Q_3 = 70.0\). **Task:** **(a) Select the correct box plot for the given data.** - **BoxPlot A:** Displays a box with the left edge near 46 and the right edge near 56, with a longer whisker extending to the right, suggesting a positive skewness. - **BoxPlot B:** Shows a box with the left edge near 50 and the right edge near 70, with short whiskers on both sides, indicating a symmetric or slight skew. Choices: - ○ BoxPlot A - ○ BoxPlot B - ○ BoxPlot C **(b) Describe its shape (skewed left, symmetric, skewed right).** - ○ The distribution is symmetric. - ○ The distribution is skewed left. - ○ The distribution is skewed right. Boxes are graphical representations used to depict the spread of a dataset using quartiles. The box itself shows the interquartile range (IQR), while the "whiskers" extend to the minimum and maximum values within 1.5 times the IQR from the upper and lower quartiles.
### Transcription and Analysis of Box Plots #### Box Plot Descriptions The image features two box plots labeled "BoxPlot B" and "BoxPlot C" that are used to visually represent the distribution, variability, and central tendency of data sets. #### BoxPlot B - **Minimum Value:** 50 - **Lower Quartile (Q1):** Approximately 60 - **Median (Q2):** Approximately 70 - **Upper Quartile (Q3):** Approximately 80 - **Maximum Value:** 90 **Description:** BoxPlot B is relatively compact, with the median closer to the upper quartile, indicating a potential left skew in data distribution. The box, representing the interquartile range, spans from around 60 to 80, with whiskers extending to 50 and 90, indicating no significant outliers. #### BoxPlot C - **Minimum Value:** 40 - **Lower Quartile (Q1):** Approximately 55 - **Median (Q2):** Approximately 70 - **Upper Quartile (Q3):** Approximately 85 - **Maximum Value:** 100 **Description:** BoxPlot C shows a wider spread of data compared to BoxPlot B. The median is centrally located within the box, suggesting a more symmetrical distribution. The interquartile range stretches from 55 to 85, with whiskers indicating a range from 40 to 100. #### Educational Purpose These box plots can be used to teach students how to interpret data visualizations, understand statistical measures such as quartiles and medians, and identify distribution characteristics such as skewness and outliers in a data set. **Website Functionality:** The interface shows navigation options to browse through other pages (Prev 13 of 19 Next) and provides controls to save, exit, or submit the current work.
Transcribed Image Text:### Transcription and Analysis of Box Plots #### Box Plot Descriptions The image features two box plots labeled "BoxPlot B" and "BoxPlot C" that are used to visually represent the distribution, variability, and central tendency of data sets. #### BoxPlot B - **Minimum Value:** 50 - **Lower Quartile (Q1):** Approximately 60 - **Median (Q2):** Approximately 70 - **Upper Quartile (Q3):** Approximately 80 - **Maximum Value:** 90 **Description:** BoxPlot B is relatively compact, with the median closer to the upper quartile, indicating a potential left skew in data distribution. The box, representing the interquartile range, spans from around 60 to 80, with whiskers extending to 50 and 90, indicating no significant outliers. #### BoxPlot C - **Minimum Value:** 40 - **Lower Quartile (Q1):** Approximately 55 - **Median (Q2):** Approximately 70 - **Upper Quartile (Q3):** Approximately 85 - **Maximum Value:** 100 **Description:** BoxPlot C shows a wider spread of data compared to BoxPlot B. The median is centrally located within the box, suggesting a more symmetrical distribution. The interquartile range stretches from 55 to 85, with whiskers indicating a range from 40 to 100. #### Educational Purpose These box plots can be used to teach students how to interpret data visualizations, understand statistical measures such as quartiles and medians, and identify distribution characteristics such as skewness and outliers in a data set. **Website Functionality:** The interface shows navigation options to browse through other pages (Prev 13 of 19 Next) and provides controls to save, exit, or submit the current work.
Expert Solution
Step 1

 

 

(a)

Observe that the exam ranged from 46 to 87.

Here minimum = 46

First quartile , Q1= 53.25

Median, Q2= 56.0

Third quartile, Q3= 70.0

Maximum = 87

step 1: Mark the points Q1=53.25 and

Q3 =70.0 and draw the rectangular box by joining these points.

Step 2: mark the median point Q2=56.0

and extend the towards upper part of the rectangular box

Step 3:

Mark the minimum point 46 and extend the line from Q1=53.25  to minimum point 46.

Step 4:

Mark the maximum point 87  and extend the line from Q3=70.0 to maximum point 87.

The box plot is displayed below.

Statistics homework question answer, step 1, image 1

The correct option is, Box plot(A).

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