analyze numerical data name · 2020-05-14 · 332 esson 29 analyze numerical data ©urriculum...

©Curriculum Associates, LLC Copying is not permitted. 329Lesson 29 Analyze Numerical Data

Name: Analyze Numerical Data

Lesson 29

Prerequisite: Use a Box Plot

Study the example showing how to display data in a box plot. Then solve problems 1–7.

1 What is the interquartile range (IQR) of the data? Does the IQR include outliers? What does the IQR tell you about the fish lengths?

2 What is the range of the data? Does the range include outliers? What does the range tell you about the fish lengths?

Example

Fishermen recorded the lengths, in inches, of fifteen fish that they caught on a fishing trip: 22, 14, 15, 3, 9, 20, 20, 11, 9, 10, 18, 19, 10, 12, 15. Make a box plot of the data.

First, order the lengths from shortest to longest.

3, 9, 9, 10, 10, 11, 12, 14, 15, 15, 18, 19, 20, 20, 22

The minimum is the least value, 3. The maximum is the greatest value, 22. The median, 14, is the middle number. The lower quartile, 10, is the middle number of all values less than the median. The upper quartile, 19, is the middle number of all values greater than the median.

0 2 4

Minimum

Lowerquartile Median

Maximum

Upperquartile

6 8 10 12 14 16 20 22 2418 Vocabularybox plot a five-number

summary that includes

the minimum, the lower

quartile, the median, the

upper quartile, and the

maximum.

lower quartile the

middle number of all

values less than the

median.

upper quartile the

middle number of all

values greater than the

median.

©Curriculum Associates, LLC Copying is not permitted.330 Lesson 29 Analyze Numerical Data

Solve.

3 The number of pounds that each kitten or cat at an animal rescue center weighs is listed below Display the data in a box plot

1, 1, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 8, 8, 10, 12

4 What are the lower quartile, the upper quartile, and the IQR for the data in problem 3?

5 Explain what the box that you drew in the box plot in problem 3 represents in terms of the weights

6 Tomas listed the amounts that he deposited in his savings account each week for 15 weeks Write the correct amount in each box below the box plot

$25, $32, $32, $35, $35, $35, $35, $38, $40, $40, $43, $43, $44, $45, $55

7 In problem 6, what do the lines to the right and to the left of the rectangular box in the box plot represent?

0 1 2 3 4 5 6 7 8Weights (pounds)

10 11 12 1514139


Name: Lesson 29

1 What is the median of this data? What does the median tell you about the heights of the trees?

2 Are there any outliers in this data set? If so, what are they? Explain

3 Explain why the median and IQR are not affected by outliers

Example

The heights of trees, in feet, in a city park are listed below

3, 13, 16, 18, 19, 21, 21, 23, 25, 25, 27, 27, 31, 33, 43

What does the IQR tell you about the variability of the heights?

Draw a box plot to help you visualize the quartile values

0 5 10 20

Height of Trees (ft)

15 25 30 35 40 45

The IQR is 27 2 18 5 9 It tells me that the middle 50% of the heights of the trees are in the 9-foot range between 18 feet and 27 feet

Use Interquartile Range to Describe Data

Study the example showing how the IQR measures variability. Then solve problems 1–7.


Solve.

Use the following situation and box plot to solve problems 4–7.

The speeds of cars, in miles per hour, along a neighborhood street were recorded and are shown in the box plot

18 20 22 2624 28 30 32 34 36 38 40 42

4 Can you tell from the box plot whether any one of the cars was traveling at a speed of 34 miles per hour?

5 Does the box plot show the number of car speeds that were recorded? Explain

6 What is the range of data shown in the box plot? What is the IQR? Explain why it might be more helpful to use the IQR rather than the range to describe this data set

7 Write a question about the distribution of car speeds that you can answer by looking at the box plot Answer your question


Name: Lesson 29

1 Look at the table Explain how the deviation from the mean was calculated for the data values 66 and 53 Why is one deviation positive and the other negative?

2 What is the MAD of the data values in the example? Explain how you found the MAD

3 What does the MAD tell you about the number of points scored?

Example

The table shows the number of points scored by a basketball team during the first 10 games of the season

66 53 48 68 71

42 56 55 49 58

The mean of this data set is 56 6 Make a table to help you find the mean absolute deviation (MAD) of the data

The mean absolute deviation (MAD) of a data set can help you understand the variability of the data in the set To help you find the MAD, make a table that shows the data values in the set, their deviations from the mean, and the absolute values of those deviations

Data Value 66 53 48 68 71 42 56 55 49 58

Deviation from Mean 9 4 23 6 28 6 11 4 14 4 214 6 20 6 21 6 27 6 1 4

Absolute Deviation 9 4 3 6 8 6 11 4 14 4 14 6 0 6 1 6 7 6 1 4

Vocabularymean absolute deviation (MAD) average distance

between each data

value and the mean It

describes how spread

out the data is

Use Mean Absolute Deviation

Study the example showing how to analyze data using the mean absolute deviation. Then solve problems 1–8.


Solve.

Use the data in the table to solve problems 4–8.

Price of Laptop Computers ($)

390 230 290 350 270

340 320 890 220 400

4 What is the mean of this data?

Show your work.

Solution:

5 What does the mean tell you about the prices of the computers?

6 What is the MAD of this data?

Show your work.

Solution:

7 What does the MAD tell you about the prices of the computers? Does the MAD tell you that there is a lot of variability in the prices or not?

8 Which data value from the table would you delete to make the greatest change possible to the MAD? Explain


Name: Lesson 29

2 In problem 1, is the mean or the median a better measure of center? Explain

1 The dot plot shows the number of books that some sixth graders read last month Find the mean and the median

Number of Books Read

0 2 4 86 10 12 14 16 18 20 22 24

Show your work.

Solution:

What does each dot on the plot represent?

How do outliers affect the measures of center?

Analyze Numerical Data

Solve the problems.

3 The histogram shows the time, to the nearest whole minute, that some students spend each week doing chores How many students spend more than

1 ·· 2 hour doing chores?

A 4 C 12

B 5 D 20

How many values are in each interval?

Nu

mb

er o

f St

ud

ents

Time (min)

Time Spent Doing Chores

1–15 16–30 31–45 46–600

2

4

6

8

10

12

14


Solve.

4 The box plot shows the amount of money raised by some students for a school fund-raiser Tell whether each statement is True or False

25 30 35 40 45 50 55 60 65

Money ($)75 80 8570

a. The variability of the middle 50% of the money raised is less than the variability of the lower 25% u True u False

b. The box plot shows that 80 students raised money u True u False

c. If the $30 value is replaced by a $50 value, the IQR will be the same u True u False

5 What is the IQR in problem 4? What does it tell you about the data values in the box plot?

6 Josh recorded the amount of time, in minutes, that he exercised during the first 10 days of the month

30, 45, 25, 25, 35, 5, 40, 35, 30, 20

The mean of the data is 29 Find the MAD of the data What does the MAD tell you?

Show your work.

Solution:

In the box plot, what does the rectangular box represent?

What does mean absolute deviation measure?

What are the five numbers represented in a box plot?

analyze numerical data name · 2020-05-14 · 332 esson 29 analyze numerical data ©urriculum...

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