Unit 4 Midterm Review

What is central tendency?

What is central tendency?

• It refers to the middle or center of the data.

What is the mean of a data set?

What is mean?

• It is called the average. • You add up all the numbers to find a sum. • You divide the sum by the total numbers in the

data set.

What is the median? How do you find it?

What is the median? How do you find it?

• It is the middle of the data. • You put the numbers in order and eliminate

one on each side of the data until you find the middle.

How do you find the median of a data set if there are more than one number in the

middle of the data set?

2 5 6 12 15 18

How do you find the median of a data set if there are more than one number in the

middle of the data set?

2 5 6 12 15 18

Find the mean of those two numbers by adding them up and dividing by two.

6 + 12 = 1818/2 = 9The median would be 9

1. Define mode. 2. What would it be for the following data set?

• 1,2,2,2,3,5,6,7

Define mode. What would it be for the following data set?

• The number that occurs most often in a data set. • 1,2,2,2,3,5,6,7• The mode would be 2, because it occurs the most often.• Some data sets don’t have a more, while some may have

more than one.

Which measure of center is affected by outliers?

• Hint: If you made a really low grade, what is going to affected the most? (Mean or Median)

Which measure of central tendency is affected by outliers?

Hint: If you made a really low grade, what is going to affected the most? (Mean or Median)

The mean is affected by outliers. The mean of the test scores will go down.

The median is not affected by outliers?

1. Which set of data would have a higher mean (average)?2. Which set of data would have a higher median?3. Which data set had an outlier?

Data set 1: 5 5 15 20 25

Data set 2: 5 5 15 20 60

• 1. Which set of data would have a higher mean (average)? - Data set 22. Which set of data would have a higher median? – They both have the same median3. Which data set had an outlier? – Data set 2

What affect will an extremely small outlier have on a set of data?

Hint: For example, if you have a really low test grade, how will this affect the mean and median for the set of data?

What affect will an extremely small outlier have on a set of data?

Hint: For example, if you have a really low test grade, how will this affect the mean and median for the set of data?

The small outlier will bring down the mean (average).

The median will not really be affected.

How will really large outliers affect the mean and median of a set of data?

How will really large outliers affect the mean and median of a set of data?

• The large outlier will cause the mean (average) to increase.

• It will not really affect the median.

• We measured the heights of the cans and created data sets.

• What happens to the measures of center after we replace the tallest can with the Pringles can?

Before

After

• We measured the heights of the cans and created data sets.

• What happens to the measures of center after we replace the tallest can with the Pringles can?

• The mean increased. • The median stayed

the same.

Before

After

Can you name a real example of how mode is used in the real world?

Can you name a real example of how mode is used in the real world?

• Voting - the candidate with the most votes, wins.

Find the Mean Absolute Deviation (MAD) for both people. Find who is

more consistent hitter. Batting Averages:Stefan: .248, .296, .325, .337, .364Damon: .287. .322, .290, .314, .302

Be sure to make a table for each baseball player.

Mean Diff Pos Diff Mean Diff Pos Diff

0.248 0.314 0.066 0.0666 0.287 0.303 -0.016 0.016

0.296 0.314 0.018 0.018 0.322 0.303 0.019 0.019

0.325 0.314 -0.011 0.011 0.29 0.303 -0.013 0.013

0.337 0.314 -0.023 0.023 0.314 0.303 0.011 0.011

0.364 0.314 -0.05 0.05 0.302 0.303 -0.001 0.001

Sum 0.1686 Sum 0.06

0.314 Count 5 0.303 Count 5

MAD 0.034 MAD 0.012

Stefan Damon

The list shows the average high temperatures for 20 cities on one February day.

69, 66, 65, 51, 50, 50, 44, 41, 38, 32, 32, 28, 20, 18, 12, 8, 8, 4, 2, 2

Complete the Frequency column in this cumulative frequency table

February Temperatures in 20 CitiesAverage

HighsFrequency Cumulative

FrequencyHint: Count the numbers that fall into each interval category, and place that total under frequency.

0–19

20–39

40–59

60–79

The list shows the average high temperatures for 20 cities on one February day. Make a cumulative frequency table of the data.

Complete the Cumulative Frequency column

Step 3: Find the cumulative frequency for each row by adding all the frequency values that are above or in that row.

February Temperatures in 20 CitiesAverage

HighsFrequency Cumulative

Frequency

0–19

20–39

40–59

60–79

7

5

5

3

7

12

17

20

A stem-and-leaf plot can be used to show how often data values occur and how they are distributed.

Each leaf on the plot represents the right-hand digit in a data value.

Stems represents left-hand digits.

2 4 7 9

3 0 6

Stems Leaves

Key: 2|7 means 27

Create a stem and leaf plot

Step 2: List the stems from least to greatest on the plot.

Stems Leaves

1234

The stems are the tens digits.

The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data.

33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17

Creating Stem and Leaf Plot

Step 3: List the leaves for each stem from least to greatest.

Stems Leaves

1234

The stems are the tens digits.

2 5 5 7 7 8

0 1 2 3 3 93 3

0

The leaves are the ones digits.

The data shows the number of years coached by the top 15 coaches in the all-time NFL coaching victories. Make a stem-and-leaf plot of the data. Then find the number of coaches who coached fewer than 25 years.

33, 40, 29, 33, 23, 22, 20, 21, 18, 23, 17, 15, 15, 12, 17

Would it be appropriate to make a stem and leaf plot for the number of

text message you send Monday through Friday?

Would it be appropriate to make a stem and leaf plot for the number of

text message you send Monday through Friday?

• No because you would be examining two variables ( number of messages, and days of the week).

• Stem and leaf plots are only appropriate when you are examining one variable, such as the number of text message, or test grades in math.

Create a line plot for the data:

M T W Th F S Su

Wk 1 0 6 4 6 5 8 2

Wk 2 2 7 7 7 0 6 8

Wk 3 0 6 8 5 6 1 2

Wk 4 4 8 4 3 3 6 0

Number of Babysitting Hours in July

Your line plot should look like this:

Step 2: Put an X above the number on the number line that corresponds to the number of babysitting hours in July.

0 1 2 3 4 5 6 7 8

XXXX

X

XXX XX

XXX XX

XXXXXX

XXX

XXXX

The greatest number of X’s appear above the number 6. This means that Morgan babysat most often for 6 hours.

Find the median of the line plot that you just created.

What is noticeable about this line plot?

What is noticeable about this line plot?

This line plot has an outlier. Which measure of central tendency best describes the data?

This line plot has an outlier. Which measure of central tendency best describes the data?The median because there is an outlier in the data set.

Which measure of central tendency should be used to describe this data set?

Which measure of central tendency should be used to describe this data set?

The mean because it data set does not have an outlier.

Which measure of central tendency should be used to describe this data set?

Which measure of central tendency should be used to describe this data set?

The median should be used because the data set has an

outlier.

Find the mean of the data setA quick way is to find the sum for each row. Add up the sum for

each row, and then divide this sum by pieces of data that are in the data set.

Find the mean of the data set

3 + 10 + 18+16+15+12 + 10

You can find the sum of each line of numbers

For example:

2 Occurs 5 times, so 2X5 = 10

= 84

---------- = 3.5

24

(24 total pieces of data – count the number of Xs)

Use the information given to complete the cumulative

frequency table

Nurses’ Ages

Ages Frequency Cumulative Frequency

20–29 5

30–39 12

40–49 16

50–59 18

60–69 20

7

5

4

2

2

What is a population?

Population = the entire group

•Researchers often study a part of the population, called a sample.

What is a sample?

Sample is a small group of the total population

What is a random sample?

•For a random sample, members of the population are chosen at random. This gives every member of the population an equal chance of being chosen.

What is a convenience sample?

CONVENIENCE SAMPLE

• A convenience sample is based on members of the population that are conveniently available, such as 30 elk in a wildlife preservation area.

•A biased sample does not fairly represent the population.

• A study of 50 elk belonging to a breeder could be biased because the breeder’s elk might be less likely to have Mad Elk Disease than elk in the wild.

Which would be better to have, a random sample or a convenience

sample?

Which would be better to have, a random sample or a convenience

sample?

A random sample is more likely to be representative of a

population than a convenience sample is.

Min - 22LQ - 24Med - 31UQ - 38Max - 42

Course 2

Box-and-Whisker PlotsData from the previous question

(min, LQ, med, UQ, max)

42 22 31 27 24 38 35

22 24 27 31 35 38 42

22 24 27 31 35 38 42

The least value.

The greatest value.

The median.

The upper and lower quartiles.22 24 27 31 35 38 42

Step 1: Order the data from least to greatest. Then find the least and greatest values, the median, and the lower and upper quartiles.

Create a box and whiskers from the 5 number summary you just

found.

Course 2

7-5 Box-and-Whisker Plots

20 22 24 26 28 30 32 34 36 38 40 42

Above the number line, plot a point for each value in Step 1.

Step 3: Draw a box from the lower to the upper quartile. Inside the box, draw a vertical line through the median.Then draw the “whiskers” from the box to the least and greatest values.

Use the box-and-whisker plots below to answer each question.

Additional Example 2A: Comparing Box-and-Whisker Plot

Course 2

7-5 Box-and-Whisker Plots

Which set of heights of players has a greater median?

64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)

Basketball Players

Baseball Players

Use the box-and-whisker plots below to answer each question.

Additional Example 2A: Comparing Box-and-Whisker Plot

Course 2

7-5 Box-and-Whisker Plots

Which set of heights of players has a greater median?

The median height of basketball players, about 74 inches, is greater than the median height of baseball players, about 70 inches.

64 66 68 70 72 74 76 78 80 82 84 86 t Heights of Basketball and Baseball Players (in.)

Basketball Players

Baseball Players

Use the box-and-whisker plots below to answer each question.

Check It Out: Example 2A

Course 2

7-5 Box-and-Whisker Plots

Which shoe store has a greater median?

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

Use the box-and-whisker plots below to answer each question.

Check It Out: Example 2A

Course 2

7-5 Box-and-Whisker Plots

Which shoe store has a greater median?

The median number of shoes sold in one week at Sage’s Shoe Store, about 32, is greater than the median number of shoes sold in one week at Maroon’s Shoe Store, about 28.

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

Find the Range of the Box and Whiskers Plot

Find the Range of the Box and Whiskers Plot

Max – min = range

100 – 20 = 80

Find the Inter quartile Range of the B&W Plot

Find the Inter quartile Range of the B&W Plot

UQ – LQ = IQR

87 – 50 = 37

What is the range of the box known as?

What is the range of the box known as?

• Interquartile range

Use the box-and-whisker plots below to answer each question.

Check It Out: Example 2B

Course 2

7-5 Box-and-Whisker Plots

Which shoe store has a greater interquartile range?

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

Use the box-and-whisker plots below to answer each question.

Check It Out: Example 2B

Course 2

7-5 Box-and-Whisker Plots

Which shoe store has a greater interquartile range?

Maroon’s shoe store has a longer box, so it has a greater interquartile range.

20 24 26 28 30 32 34 36 38 40 42 44 t Number of Shoes Sold in One Week at Each Store

Maroon’s Shoe Store

Sage’s Shoe Store

I would like to create a graph to show the number of cancer cases world

wide from 1950 to 2011. What kind of graph would be best?

I would like to create a graph to show the number of cancer cases world

wide from 1950 to 2011. What kind of graph would be best?

• Line graph because it shows change over time

What kind of graphs should I use if percents or populations are involved?

What kind of graphs should I use if percents or populations are involved?

• Circle graph

If I want to create a display to show the number of cell phone messages

sent from Monday – Friday, what kind of graph would be best?

If I want to create a display to show the number of cell phone messages

sent from Monday – Friday, what kind of graph would be best?

• Line Graph – it shows change over time

If I wanted to create a display to show test scores in math, SS, science, and LA, what

kind of graph would be best?

If I wanted to create a display to show test scores in math, SS, science, and LA, what

kind of graph would be best?

• Bar Graph – each set of data (subject) is not related to the other

I want to create a display to show the classes grade on the final exam. What

kind of graphs would be the best?

I want to create a display to show the classes grade on the final exam. What

kind of graphs would be the best?• Stem and Leaf• Line Plot• or histogram