Math 16 Homework 13 (reviewing boxplots)

Reviewing Box-Plots

​You need to have your calculator and a piece of paper with you to complete this review homework assignment

**One problem is indicated in RED that must be turned in on paper as part of this review assignment

Each section of a box-plot contains 25% of the data

The length of each section tells you if the data is spread out or compact

This boxplot is skewed right with two outliers indicated by the *'s. Notice that the left two sections are much narrower together than the right two sections, so that means the data is more compact in that range.

SOCS

for describing​

The data in group #1 is much more variable and its median is higher than the others which are relatively similar in the 800's. Only #3 has outliers present and it is skewed right while the others are mostly symmetrical

Multiple Select

The boxplots to the left demonstrate age of Oscar winning actors by gender where A is that of female actors and B is that of male actors

Which two descriptions are correct?

• both sets of data are symmetrical with outliers in the higher ages

• The female ages are skewed left

• The males have higher ages in general such that over 50% of the winners are older than 75% of the female winners

• The female ages are more variable than the males

​Both boxplots are symmetrical with outliers in the higher ages [if you ignore the *'s, everything else is pretty balanced]

​

The males have higher ages in general such that 50% of the males are older than 75% of the female winners [notice that three female sections are below the median line of the males]

Multiple Choice

Which item of a boxplot is also at the 25th percentile?

• Minimum

• Q1

• Median

• Q3

Multiple Choice

Which item is also known as the IQR?

• Median

• Q3 - Q1

• 1.5

• Maximum

Multiple Choice

Which of the following is how a person could determine the range of the data from its boxplot?

• Q3 - Q1

• Median*2

• Maximum - Minimum

• Minimum + Maximum

​Answers:

​-For each section containing 25% of the data, the 25th percentile would be at Q1 (minimum to Q1 contains 25%)

-The IQR or inter-quartile range is how wide the box is which is found with Q3 - Q1

​-The range of data is how wide it is, so Maximum - Minimum would determine the range

Enter the data below and use statplot to view the boxplot of the data to answer questions:

23, 52, 67, 18, 60, 78, 81, 12, 25, 26, 153, 40, 51, 72, 60, 68

Multiple Choice

Which shape best describes the boxplot?

• Skewed left

• Skewed right

• Symmetrical with one outlier

Multiple Select

Which two sections of the boxplot have the most compact data?

• Between minimum and Q1

• Between Q1 and median

• Between median and Q3

• Between Q3 and Maximum

Multiple Choice

Use the trace button and identify the median value

• 56

• 70

• 25.5

Determing outliers by hand

​1.5(IQR) = 1.5(Q3-Q1) = #

Q1 - # = lower boundary

Q3 + # = upper boundary

Any numbers outside the boundaries are outliers​

​

​

Using the same data below, find the five-number summary using 1-VarStats to answer some questions and then perform outlier math

23, 52, 67, 18, 60, 78, 81, 12, 25, 26, 153, 40, 51, 72, 60, 68

​#1 This problem must be turned in with the appropriate work. You must include (1) a list of the 5-number summary, (2) outlier math clearly shown, and a (3) carefully drawn boxplot

Multiple Select

Which of the following make up the five-number summary?

• min=12, max=153

• Q1=25.5, Q3=70

• $$\overline{x}$$ =55.375,

  $$S_x$$ =34.34 

• Median = 56

Multiple Select

Perform the outlier math to determine the upper and lower boundaries

Q1=25.5, Q3=70

• 66.75 = IQR

• -41.25 = LB

• 136.75 = UB

• 153 = UB

Multiple Choice

With an upper boundary of 136.75, this means we have ___outlier(s)

• 0

• 1

• Many

153 is the only data item outside of either boundary, so there is exactly 1 outlier

​1.5(70-25.5) = 66.75

​

25.5-66.75 = -41.25 LB

70+66.75 = 136.75 UB​

summary:

Some text here about the topic of discussion

Knowing 153 is an outlier and would be indicated with a *, where would the right-side arm extend to? [question must be answered on the next slide]

23, 52, 67, 18, 60, 78, 81, 12, 25, 26, 153, 40, 51, 72, 60, 68

Multiple Choice

Where would the right arm extend to?

• 136.75

• 153

• 81

81 because it is the next largest number that is not outside the boundary

​Woo Hoo! The End!

​Be sure to turn in your work on paper in class OR attached to the Google Classroom if you are absent the day it was due

~Mrs. Hatch, 2025

" Only one more homework assignment left
~ in this course! "