Lesson 1.8 Boxplots & Percentile Content Check

Instructions

Work with your table group, read, discuss and answer questions.

Required

1

Here are the scores of Mrs. Liao’s students on their first statistics test:
Here are the data:

93 93 87.5 91 94.5 72 96 95 93.5 93.5 73 82 45 88 80 86
85.5 87.5 81 78 86 89 92 91 98 85 82.5 88 94.5 43

Use statsmedic.com/applets (1 quantitative variable, single group) to create a boxplot of the data values and insert it into the 'show your work' section. Copy and paste the data from formative into statsmedic.com/applets.

Do NOT take a screen shot, only take a 'snip' of the boxplot. Ask your table if you are not sure how.

Required

1

How did the students do on Mrs. Liao’s first test?
Use the boxplot from #1 to help justify your answer.
Use percents and quartiles in your answer.

Required

4

The dotplot shows the number of calories per serving for 16 brands of frozen cheese pizza. Identify any outliers in the distribution. Show your work by filling in the values below.

 Use statsmedic.com/applets to create a boxplot and show the 5# summary. You will need to identify the 16 data values and enter them into statsmedic. Work with a partner!
Remember to enter 310 three times since there are three dots, same with 320, 340, 350 and 360.

1. Calculate the IQR.  IQR = _______ do not use units
2. Upper limit = _______ 
3. Lower limit = _______ 
4. Are there any outliers? Yes or No? _______ 

Required

4

The roster of the Dallas Cowboys professional football team in a recent season included 7 defensive linemen. Their weights (in pounds) were:

 321, 285, 300, 285, 286, 293,  298 

Use statsmedic.com/applets to create a boxplot and show the 5# summary.

1. Calculate the IQR.  IQR = _______ do not use units
2. Upper limit = _______ 
3. Lower limit = _______ 
4. Are there any outliers? Yes or No? _______ 

Required

1

A new player was drafted to the Dallas Cowboys defensive line. He weighed in at 328 pounds.
Is he an outlier and how do you know?

Required

1

Look at your boxplot for #3. Which measure of variability—the IQR or standard deviation—would you report for these data?
Use the boxplot from #3 to help answer.

Required

4

Required

1

In its May 2010 edition,Consumer Reports magazine rated different types of refrigerators, including those with bottom freezers, those with top freezers, and those with side freezers. One of the variables they measured was annual energy cost (in dollars).
The following boxplots show the energy cost distributions for each of the refrigerator types.

What percentage of just the bottom freezers(look at the top boxplot) cost more than $60 per year to operate? Use units.

Required

1

What percentage of the side freezers(look at the middle boxplot) cost more than $60 per year to operate?

Required

1

What percentage of top freezers(look at the bottom boxplot) cost more than $60 per year to operate?

Required

3

Using the boxplots shown in #8, give one comparison of the three refrigerators using % if possible.
Do not use the information from #8-10.
Ex. you can compare the medians, Q3's, ranges, Min and Max, etc.
Use COMPARATIVE language.

Required

3

In a September 28, 2008, article titled, “Letting Our Fingers Do the Talking,” the New York Times reported that Americans now send more text messages than they make phone calls. Mr. Williams was curious about whether this claim was valid for high school students. 
So he collected data from his first-period statistics class on the number of text messages and calls they had sent or received in the past 24 hours. 
A boxplot of the difference (Texts – Calls) in the number of texts and calls for each student is shown here. 

Remember, higher numbers indicate a bigger difference in the number of texts sent minus phone calls.

Roughly what percent of the data values are a difference of less than 20 texts-calls?  _______ Use % in your answer.
How many outliers are shown in the boxplot?  _______ 
Roughly what percent of the data values are a difference of less than 0 texts-calls?  _______ 
Use % in your answer. 

Required

1

In a September 28, 2008, article titled, “Letting Our Fingers Do the Talking,” the New York Times reported that Americans now send more text messages than they make phone calls. Mr. Williams was curious about whether this claim was valid for high school students.
So he collected data from his first-period statistics class on the number of text messages and calls they had sent or received in the past 24 hours.
A boxplot of the difference in the number of texts and calls for each student (Texts – Calls) is shown below.

Do these data support the claim in the article about texting versus calling?
Justify your answer.
Remember, higher numbers indicate a bigger difference in the number of texts sent minus phone calls.

Ex.
'These data do/do not support the claim in the article because... '

Required

1

The dotplot shows the number of wins for each of the 30 Major League Baseball teams in the 2014 season:

Percentile means:
the percent of data values that are less than a given data value.

Ex. There is data at 76 wins. To find the percentile for 76 wins:
1. count the number of data values less than 76 (this is 9)
2. Make a fraction with the total number of values on the bottom and the number to the left on the top.
3. Divide the fraction, this decimal is the percentile, you can multiply by 100 if you would like to.

Find the percentile for the Boston Red Sox, who won 71 games. Hint: find the data value for 71 wins, count how many values are less than (to the left) of that dot.
Set this up as a fraction with the total on the bottom, divide.
Multiply by 100 to get a percent.

Round your answer to one place past the decimal point.
Include the % sign.

Required

1

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
Interpret this value in context.

Required

1

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
How many games did New York win?
Hint: what is 60% of 30? This tells you where their value is in the dotplot above compared to the other data, then look just to the right of your answer.

How many pairs of shoes does a typical teenage boy own? To find out, a group of statistics students surveyed a random sample of 20 male students from their large high school. Then they recorded the number of pairs of shoes that each boy owned. 
Here are the data:
14, 7, 6, 5, 12, 38, 8, 7, 10, 10, 10, 11, 4, 5, 22, 7, 5, 10, 35, 7

Copy and paste the list into statsmedic.com/applets

Required

2

Martin is the student who reported owning 22 pairs of shoes. Observe a dotplot in statsmedic.com/applets of the data distribution.
Find Martin’s percentile.

Martin's percentile is: _______ express the percentile as a percent with the % symbol

Emanuel just had a growth spurt and most of his shoes don't fit. He currently has 6 pairs of shoes. Find Emanuel's percentile.

Emanuel's percentile is: _______ express the percentile as a percent with the % symbol

Required

1

Using the information on pairs of shoes:
There is a student who is at the 75th%, how many shoes does this student have?

Hint: how many is 75% of 20? Use a calculator.
Using the dotplot in statsmedic.com/applets, count in that many dots. Look at the value for the next dot to the right.

How many pairs of shoes does George have?

Required

7

Draggable item		Corresponding Item

Required

5

Match the data distributions with the correct measure of center & variability based on their shape:

Item 2
Item 1

Required

1

Draggable item		Corresponding Item
IQR		Exreme value that doesn't appear to belong with the rest of the data.
Standard Deviation		The middle value in the data set when ordered least to greatest. 50% of the data is less and 50% of the data is greater than the median.
Mean		The average of the data values
Q3		Interquartile Range- the range of the middle 50% of the data values.
Outlier		The average distance from the mean of all the data values.
Q1		1st quartile, 25% of the data is less than Q1
Median		3rd quartile, 75% of the data is less than Q3

Lesson 1.8 Boxplots & Percentile Content Check

How did the students do on Mrs. Liao’s first test?
Use the boxplot from #1 to help justify your answer.
Use percents and quartiles in your answer.

A new player was drafted to the Dallas Cowboys defensive line. He weighed in at 328 pounds.
Is he an outlier and how do you know?

Look at your boxplot for #3. Which measure of variability—the IQR or standard deviation—would you report for these data?
Use the boxplot from #3 to help answer.

What percentage of the side freezers(look at the middle boxplot) cost more than $60 per year to operate?

What percentage of top freezers(look at the bottom boxplot) cost more than $60 per year to operate?

Using the boxplots shown in #8, give one comparison of the three refrigerators using % if possible.
Do not use the information from #8-10.
Ex. you can compare the medians, Q3's, ranges, Min and Max, etc.
Use COMPARATIVE language.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
Interpret this value in context.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
How many games did New York win?
Hint: what is 60% of 30? This tells you where their value is in the dotplot above compared to the other data, then look just to the right of your answer.

Match the data distributions with the correct measure of center & variability based on their shape:

How did the students do on Mrs. Liao’s first test?
Use the boxplot from #1 to help justify your answer.
Use percents and quartiles in your answer.

A new player was drafted to the Dallas Cowboys defensive line. He weighed in at 328 pounds.
Is he an outlier and how do you know?

Look at your boxplot for #3. Which measure of variability—the IQR or standard deviation—would you report for these data?
Use the boxplot from #3 to help answer.

The following boxplots summarize data on the amount of fat (in grams) in 12 McDonald’s beef sandwiches and 9 McDonald’s chicken or fish sandwiches.

Compare the distributions of fat content for the two types of sandwiches. Use the boxplots above. Select all that are correct, there are four.

What percentage of the side freezers(look at the middle boxplot) cost more than $60 per year to operate?

What percentage of top freezers(look at the bottom boxplot) cost more than $60 per year to operate?

Using the boxplots shown in #8, give one comparison of the three refrigerators using % if possible.
Do not use the information from #8-10.
Ex. you can compare the medians, Q3's, ranges, Min and Max, etc.
Use COMPARATIVE language.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
Interpret this value in context.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
How many games did New York win?
Hint: what is 60% of 30? This tells you where their value is in the dotplot above compared to the other data, then look just to the right of your answer.

Match the vocabulary word with its meaning.

Match the data distributions with the correct measure of center & variability based on their shape:

Given the summary statistics below from Statsmedic.com/applets:
What do you know about the shape of the data distribution? Pick two correct answers.

Lesson 1.8 Boxplots & Percentile Content Check

Lesson 1.8 Boxplots & Percentile Content Check

How did the students do on Mrs. Liao’s first test? Use the boxplot from #1 to help justify your answer.Use percents and quartiles in your answer.

A new player was drafted to the Dallas Cowboys defensive line. He weighed in at 328 pounds.Is he an outlier and how do you know?

Look at your boxplot for #3. Which measure of variability—the IQR or standard deviation—would you report for these data? Use the boxplot from #3 to help answer.

What percentage of the side freezers(look at the middle boxplot) cost more than $60 per year to operate?

What percentage of top freezers(look at the bottom boxplot) cost more than $60 per year to operate?

Using the boxplots shown in #8, give one comparison of the three refrigerators using % if possible. Do not use the information from #8-10. Ex. you can compare the medians, Q3's, ranges, Min and Max, etc. Use COMPARATIVE language.

The New York Yankees’ number of wins is at the 60th percentile of the distribution. Interpret this value in context.

The New York Yankees’ number of wins is at the 60th percentile of the distribution. How many games did New York win?Hint: what is 60% of 30? This tells you where their value is in the dotplot above compared to the other data, then look just to the right of your answer.

Match the data distributions with the correct measure of center & variability based on their shape:

How did the students do on Mrs. Liao’s first test? Use the boxplot from #1 to help justify your answer.Use percents and quartiles in your answer.

A new player was drafted to the Dallas Cowboys defensive line. He weighed in at 328 pounds.Is he an outlier and how do you know?

Look at your boxplot for #3. Which measure of variability—the IQR or standard deviation—would you report for these data? Use the boxplot from #3 to help answer.

The following boxplots summarize data on the amount of fat (in grams) in 12 McDonald’s beef sandwiches and 9 McDonald’s chicken or fish sandwiches.Compare the distributions of fat content for the two types of sandwiches. Use the boxplots above. Select all that are correct, there are four.

What percentage of the side freezers(look at the middle boxplot) cost more than $60 per year to operate?

What percentage of top freezers(look at the bottom boxplot) cost more than $60 per year to operate?

Using the boxplots shown in #8, give one comparison of the three refrigerators using % if possible. Do not use the information from #8-10. Ex. you can compare the medians, Q3's, ranges, Min and Max, etc. Use COMPARATIVE language.

The New York Yankees’ number of wins is at the 60th percentile of the distribution. Interpret this value in context.

The New York Yankees’ number of wins is at the 60th percentile of the distribution. How many games did New York win?Hint: what is 60% of 30? This tells you where their value is in the dotplot above compared to the other data, then look just to the right of your answer.

Match the vocabulary word with its meaning.

Match the data distributions with the correct measure of center & variability based on their shape:

Given the summary statistics below from Statsmedic.com/applets:What do you know about the shape of the data distribution? Pick two correct answers.

How did the students do on Mrs. Liao’s first test?
Use the boxplot from #1 to help justify your answer.
Use percents and quartiles in your answer.

A new player was drafted to the Dallas Cowboys defensive line. He weighed in at 328 pounds.
Is he an outlier and how do you know?

Look at your boxplot for #3. Which measure of variability—the IQR or standard deviation—would you report for these data?
Use the boxplot from #3 to help answer.

Using the boxplots shown in #8, give one comparison of the three refrigerators using % if possible.
Do not use the information from #8-10.
Ex. you can compare the medians, Q3's, ranges, Min and Max, etc.
Use COMPARATIVE language.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
Interpret this value in context.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
How many games did New York win?
Hint: what is 60% of 30? This tells you where their value is in the dotplot above compared to the other data, then look just to the right of your answer.

How did the students do on Mrs. Liao’s first test?
Use the boxplot from #1 to help justify your answer.
Use percents and quartiles in your answer.

A new player was drafted to the Dallas Cowboys defensive line. He weighed in at 328 pounds.
Is he an outlier and how do you know?

Look at your boxplot for #3. Which measure of variability—the IQR or standard deviation—would you report for these data?
Use the boxplot from #3 to help answer.

The following boxplots summarize data on the amount of fat (in grams) in 12 McDonald’s beef sandwiches and 9 McDonald’s chicken or fish sandwiches.

Compare the distributions of fat content for the two types of sandwiches. Use the boxplots above. Select all that are correct, there are four.

Using the boxplots shown in #8, give one comparison of the three refrigerators using % if possible.
Do not use the information from #8-10.
Ex. you can compare the medians, Q3's, ranges, Min and Max, etc.
Use COMPARATIVE language.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
Interpret this value in context.

The New York Yankees’ number of wins is at the 60th percentile of the distribution.
How many games did New York win?
Hint: what is 60% of 30? This tells you where their value is in the dotplot above compared to the other data, then look just to the right of your answer.

Given the summary statistics below from Statsmedic.com/applets:
What do you know about the shape of the data distribution? Pick two correct answers.