Statistical Variable

Test Review: One-Variable and Two-Variable Statistics

Distribution of Data

Skewed Left, Skewed Right, Symmetrical

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM 
• SYMMETRICAL

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

Which of the following best describes the shape of the distribution?

• SKEWED LEFT
• SKEWED RIGHT
• UNIFORM
• SYMMETRICAL

Multiple Choice

Which statement best describes this distribution?

• Symmetrical or "Bell-Shaped"

• Symmetrical with a U shape

• Skewed Left

• Skewed Right

Multiple Choice

What is the shape of the data?

• symmetrical

• skewed left

• skewed right

• bell curve

Multiple Choice

What is the shape of the data?

• symmetrical

• skewed left

• skewed right

• bell curve

Spread, Range, Variability

The mean is always affected by the outliers.

Multiple Choice

What measure best describes the center of the data distribution?
*Hint - If the data is uniform or symmetric, the use either mean or median.  If the data is skewed, then use the median.

• spread
• mean
• peak
• median

Multiple Choice

What is the standard deviation for the data given:
5, 10, 7, 12, 0, 20, 15, 22, 8, 2

• 6.89
• 10.1
• 7.26
• 9

Multiple Choice

Given the data: 21, 31, 26, 24, 28, 26. Find the standard deviation.

• S.D. ≈ 9.67

• S.D. ≈ 26

• S.D. ≈ 3.1

• S.D. ≈ 10

Multiple Choice

Calculate the interquartile range of the following data17, 18, 18, 19, 20, 21, 21, 23, 25

• 3
• 4
• 5
• 8

Multiple Choice

The table shows the points earned by contestants in a competition. Find the range and the interquartile range of the points.

• Range: 15

  IQR: 10

• Range: 15

  IQR: 11

• Range: 15

  IQR: 12

• Range: 15

  IQR: 13

Multiple Choice

Find the median, first quartile, third quartile, and interquartile range of the data.

32, 53, 72, 66, 47, 54, 49, 67, 71

• Median: 54

  First Quartile: 49

  Third Quartile: 67

  IQR: 18

• Median: 54

  First Quartile: 48

  Third Quartile: 69

  IQR: 21

• Median: 54

  First Quartile: 48

  Third Quartile: 69

  IQR: 22

• Median: 54

  First Quartile: 49

  Third Quartile: 69

  IQR: 20

Multiple Choice

• the speed on Hayes Road is greater than the speed on Jefferson Road

• the speed on Jefferson Road is greater than the speed on Hayes Road

• these data sets contain no outliers

• the center of the data set are the same

Mean and Median

Multiple Select

The two measures of center we've study this unit are...

• Interquartile Range

• Mean Absolute Deviation

• Mean

• Median

• Standard Deviation

Multiple Select

The given data represents the ages of two softball teams. The data is represented by the box-and-whisker plots below.

Select all of the following statements about these data sets that are true.

• The data sets have the same lower quartiles.

• Since data set 1 is skewed right, the mean is more than the median.

• The data sets have the same median but different means.

• The data sets have the same mean but different medians.

• The data sets have the same interquartile range but different ranges.

Multiple Choice

Jovani worked at a local burger joint during the summer. The money he earned for the first 5 weeks is given below.

$41, $81, $39, $41, $67

Jovani then earned $23 in the sixth week. How were the mean and median affected?

• The mean and the median both decreased.

• The median and the mean both remained the same.

• The median decreased, and the mean remained the same.

• The mean decreased, and the median remained the same.

Multiple Choice

What is the interquartile range (IQR) of the data set?

• 20

• 25

• 5

• 10

Multiple Choice

Which city, Nashville or Dallas, has the smallest minimum temperature?

• Nashville

• Dallas

Multiple Choice

What is the value of the upper quartile (Q3)?

• 3

• 8

• 10

• 15

Multiple Choice

What is the maximum value?

• 3

• 8

• 10

• 18

Multiple Choice

Find the mean of the data:

17, 27, 26, 2, 1, 21, 13, 16, 19, 5, 7

• 10.5

• 21

• 14

• 6

Multiple Choice

Which car club has the higher median?

• Cruisers
• Car Hops

Outliers

Multiple Choice

Find all possible outliers for the following set of 15 data items:

108, 31, 75, 87, 79, 88, 89, 118, 51, 89, 174, 95, 51, 70, and 73.

• 31

• 174

• 31 and 174

• There are no outliers

Multiple Choice

The box plots gives information about the time, in hours, taken by a random sample of male and female runners to complete a marathon.

One of the box plots has an outlier. What is the value of that outlier?

• 8.9 hours

• 9 hours

• 7.4 hours

• 6.2 hours

Multiple Choice

Use the 1.5 IQR rule to determine if there are any outliers for the following numbers:
84, 88, 72, 74, 98, 16, 94 

• Yes, 16 is an outlier.
• Yes, 33 is an outlier.
• Yes, 98 is an outlier.
• There are no numbers less than 39 or greater than 124, therefore there are no outliers.

Multiple Choice

Which value(s) are outlier(s) for the age of male Oscar winners?

• 80

• 76

• 60

• 29

Multiple Choice

When using IQR to find outliers, which formula will identify the lower limit?

• Q3 - 1.5(IQR)

• Q1 + 1.5(IQR)

• Q1 - 1.5(IQR)

• Q3 + 1.5(IQR)

Multiple Choice

The data set below has an outlier of 42.

2, 5, 12, 15, 19, 4, 6, 11, 16, 18, 12, 12, 42

What effect does removing the outlier have on the measures of center?

• The median will decrease

• The mean will decrease

• The mean will increase

• The median will increase

Multiple Choice

If 20 is added to the data set below, which statement will be true?

50, 55, 55, 60, 62

• The median will be 20

• The mode will increase

• The mean will increase

• The mean will decrease

Multiple Choice

The data set below has an outlier of 42.

2, 5, 12, 15, 19, 4, 6, 11, 16, 18, 12, 12, 42

What effect does removing the outlier have on the distribution of the data?

• The mean will decrease

• The median will decrease

• The mean will increase

• The median will increase

Multiple Choice

When using IQR to find outliers, which formula will identify the lower limit?

• Q3 - 1.5(IQR)

• Q1 + 1.5(IQR)

• Q1 - 1.5(IQR)

• Q3 + 1.5(IQR)

Box Plot

Interpreting the Q₁, median, Q₂, max and min

Multiple Choice

What is the median test score on the 6TH Grade Math Test?

• 78

• 85

• 93

• 97

Multiple Choice

• A

• B

• C

• D

Multiple Choice

What is the best description of the data for Mr. Carson's class?

• A total of 25% of the students had 70 or more coins in their piggy banks.

• A total of 75% of the students had 25 or more coins in their piggy bank.

• A total of 25% of the students had 50 or less coins in their piggy bank.

• A total of 75% of the students had 60 or less coins in their piggy banks.

Multiple Choice

• A

• B

• C

• D

Multiple Choice

What percent of students have a height between 58 inches and 60 inches?

• 25%

• 50%

• 75%

• 100%

Multiple Choice

The box-and-whisker plot displays the number of inches of snowfall last year for 14 cities. Each city had a different amount of snowfall.

What percent of the cities had more than 64 inches of snow?

• 64%

• 50%

• 75%

• 70%

Multiple Choice

The middle 50% of scores were between....

• 30-39

• 30-50

• 39-55

• 50-68

Multiple Choice

What percentage of students scored a 39 or higher?

• None

• 25%

• 50%

• 75%

Two variable Statistics

Line of Best Fit, Linear Regression, Exponential Regression, Interpolation, Extrapolation

Multiple Choice

If the line of regression is y = 3.45x - 6.7 and the actual point is (5,12), what is the residual for that point?

• 1.45

• -1.45

• 34.7

• -34.7

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Multiple Choice

How do you calculate a residual?

• Observed - Predicted
• Predicted - Observed

Multiple Choice

Estimate the correlation coefficient

• r = 1

• r = -1

• r ≈ -0.8

• r ≈ 0.8

• r ≈ -0.5

Multiple Choice

Estimate the correlation coefficient.

• r is close to zero

• r is close to -1

• r is close to 1

• r is close to -1.5

• r is close to 1.5

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = 1.2

• B) r = 0.89

• C)r = 0

• D) r = -0.89

Multiple Choice

Car weight and distance traveled using a full tank of gas.  $$r=-.86$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Temperature of a rubber band and distance the rubber band can stretch. $$r=.84$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Number of steps taken per day and number of kilometers walked per day. $$r=.92$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Write the linear regression equation for the following data points. Round to the nearest hundredth.

• $$y=-0.83x+0.61$$

• $$y=-0.83x+0.63$$

• $$y=0.83x+-0.8$$

• $$a^2+b^2=c^2$$

Multiple Choice

Rich is a member of a gym. He pays a monthly fee plus a per-visit fee. The equation below represents the monthly amount Rich pays for his membership to the gym per month for x visits.

y= 10 + 3x

What does the y-intercept of the graph of this equation represent?

• The monthly fee

• How much Rich pays per visit

• The number of times Rich goes to the gym

• The total cost at the end of the month

Multiple Choice

What is the line of best fit?

• f(x)= 5x+1.82
• cannot be determined
• f(x)= 1.82x + 5.02
• f(x)= 1.1x + 4.2

Multiple Choice

The annual profits for a company are given in the following table, where x represents the number of years since 1992, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the year in which the profits would reach 378 thousand dollars.

• 2029

• 2014

• 2003

• 8753

Multiple Choice

The scatter plot shows the relationship between the number of chapters and the total number of pages for several books.  Use the trend line to predict how many chapters would be in a book with 180 pages. 

• 12 chapters
• 15 chapters
• 18 chapters
• 21 chapters

Multiple Choice

A restaurant sells pizza for the prices in the data table.  Calculate the linear regression equation of the data.

• y = 1.5x + 12
• y = 12x + 1.5
• y = 0.67x - 8
• y = -8x + 0.67

Multiple Choice

Data was collected on the weight of a male laboratory rat for the first 25 weeks after its birth. The linear regression equation is

y= 40x+100, where x is number of weeks and y is weight in grams.

What does the y-intercept mean in context of the problem?

• The predicted weight of the rat in year 0.

• The predicted weight of the rat at birth.

• The current weight of the rat.

• The average increase in the rat's weight.

Multiple Choice

Data was collected on the weight of a male laboratory rat for the first 25 weeks after its birth. The linear regression equation is

y= 40x+100, where x is number of weeks and y is weight in grams.

What does the y-intercept mean in context of the problem?

• The predicted weight of the rat in year 0.

• The predicted weight of the rat at birth.

• The current weight of the rat.

• The average increase in the rat's weight.