STATS Lesson 2.2

Multiple Choice

What is the purpose of transforming data when analyzing the distribution of a quantitative variable?

• To make the data more complex

• To simplify the data

• To better understand the distribution

• To eliminate outliers

Multiple Choice

What happens to the measures of center (mean and median) when a constant is added to a data set?

• They decrease by the constant.

• They remain the same.

• They increase by the constant.

• They double.

Multiple Choice

The mean test score for a class was 76 with a standard deviation of 5 points, and the shape was skewed left. The teacher decides to add 4 points to every students test score. What is the new mean, standard deviation, and shape for the distribution of test scores?

• mean=80, SD=5, shape is skewed left

• mean=80, SD=9, shape is skewed left

• mean=80, SD=5, shape is more skewed left

• mean=80, SD=9, shape is approx. symmetric

Multiple Choice

What is the effect on the variability of a distribution when a constant is added?

• It increases.

• It decreases.

• It stays the same.

• It becomes zero.

Multiple Choice

What happens to the distribution of a data set when the same positive number is added to each value?

• The distribution shifts to the right by that number.

• The distribution shifts to the left by that number.

• The distribution becomes more variable.

• The shape of the distribution changes.

Multiple Choice

Which of the following is NOT affected by adding or subtracting a constant from each observation in a data set?

• Measures of center

• Measures of location

• Measures of variability

• Five-number summary

Multiple Choice

What remains unchanged when a constant is added to or subtracted from each data value in a distribution?

• The mean

• The range

• The median

• The five-number summary

Multiple Choice

What is the effect of multiplying each adjusted test score by 2 in Mr. Tabor's example?

• It halves the scores.

• It doubles the scores.

• It adds 10 to each score.

• It subtracts 5 from each score.

Multiple Choice

What happens to the measures of center, location, and variability when data values are multiplied by a constant?

• They remain the same.

• They are halved.

• They are doubled.

• They are tripled.

Multiple Choice

What happens to the measures of center and location when each data value is multiplied by a constant b?

• They are divided by b

• They remain unchanged

• They are multiplied by b

• They are squared

Multiple Choice

How does multiplying each data value by a constant $ b $ affect the measures of variability?

• It adds b to them

• It multiplies them by b

• It subtracts b from them

• It divides them by b

Multiple Choice

What is the effect on the shape of the distribution when each data value is multiplied by a constant b?

• The shape becomes skewed

• The shape becomes normal

• The shape does not change

• The shape becomes uniform

Multiple Choice

What happens to the shape of the distribution of z-scores when standardized?

• It becomes skewed to the right

• It remains the same

• It becomes a normal distribution

• It becomes a uniform distribution

Multiple Choice

Which of the following does not change when a constant is added to a data set?

• Mean

• Median

• Range

• Maximum

Multiple Choice

The mean test score for a class was 76 with a standard deviation of 5 points, and the shape was skewed left. The teacher decides to add 4 points to every students test score. What is the new mean, standard deviation, and shape for the distribution of test scores?

• mean=80, SD=5, shape is skewed left

• mean=80, SD=9, shape is skewed left

• mean=80, SD=5, shape is more skewed left

• mean=80, SD=9, shape is approx. symmetric

Multiple Choice

If 30 is added to every observation in a data set, the only one of the following that is not changed is

• the mean

• the 75th percentile

• the median

• the standard deviation

• the minimum

Multiple Select

SELECT ALL that will change if you multiply all of the data by a constant

• mean

• median

• range

• IQR

• standard deviation

Multiple Choice

A 50 point test had a mean of 42 with a standard deviation of 5 points. The original shape of the distribution of test scores was approximately symmetric. The teacher decides to multiply all scores by 2 (so the total is out of 100). What is the new mean, standard deviation and shape for the distribution of test scores?

• mean=84, SD=10, approx. symmetric

• mean=84, SD=5, approx. symmetric

• mean=42, SD=5, approx. symmetric

• mean=84, SD=10, slightly skewed right

Multiple Choice

If 30 is added to every observation in a data set, the only one of the following that is not changed is

• the mean

• the 75th percentile

• the median

• the standard deviation

• the minimum

Multiple Select

SELECT ALL that will change if you multiply all of the data by a constant

• mean

• median

• range

• IQR

• standard deviation

Multiple Choice

A 50 point test had a mean score of 39 with a standard deviation of 4 points. The original shape of the distribution of test scores was approximately symmetric. The teacher decides to multiply all scores by 2 (so the total is out of 100) and then also add 3 points. What is the new mean, standard deviation and shape for the distribution of test scores?

• mean=81, SD=8, approx. symmetric

• mean=81, SD=11, approx. symmetric

• mean=78, SD=8, approx. symmetric

• mean=81, SD=4, approx. symmetric

Multiple Choice

For which option below would the shape of a distribution change?

• Adding transformations

• Multiplying transformations

• Shape never changes

• Logarithm transformations

Multiple Choice

Fill in the Blanks: Multiplying a constant to every data value ______ (to) measures of center/position and _________ (to) measures of spread.

• multiplies, multiplies

• multiplies, doesn't affect

• doesn't affect, multiplies

• doesn't affect, doesn't affect

Multiple Choice

The average on the Unit 1 test is 85 with a standard deviation of 10. Ms Lightbody (almost Maynard) adds ten points to everyone's score. What is the new mean?

• 95

• 85

• 20

• 10

Multiple Choice

The average on the Unit 1 test is 85 with a standard deviation of 10. Ms Lightbody (almost Maynard) adds ten points to everyone's score. What is the new standard deviation?

• 95

• 85

• 20

• 10

Multiple Choice

The average on the Unit 1 test is 85 with a standard deviation of 10. Ms Lightbody (almost Maynard) divides everyone's score by 2. What is the new mean?

• 85

• 42.5

• 170

• 5

Multiple Choice

The average on the Unit 1 test is 85 with a standard deviation of 10. Ms Lightbody (almost Maynard) divides everyone's score by 2. What is the new standard deviation?

• 2

• 10

• 5

• 20

Multiple Choice

Why doesn't addition / subtraction affect the measures of spread?

• Wait, it doesn't?

• The dataset is shifted left or right, the space between the data values isn't affected.

• The dataset is affected by addition and subtraction.

• None of these are correct answers

Multiple Choice

The heights of giraffes in feet are converted to inches by multiplying by 12. How will this affect the standard deviation?

• The SD will not be affected

• SD + 12

• 12 x SD

• 12 x SD + 12

Multiple Choice

Fill in the Blanks: Adding a constant to every data value ______ to measures of center/position and _________ measures of spread.

• adds, adds

• doesn't affect, adds

• adds, doesn't affect

• doesn't affect, doesn't affect

Multiple Choice

Fill in the Blanks: Subtracting a constant to every data value ______ (to) measures of center/position and _________ (to) measures of spread.

• subtracts, subtracts

• subtracts, doesn't affect

• doesn't affect, subtracts

• doesn't affect, doesn't affect

Multiple Choice

The mean test score for a class was 76 with a range of 20 points, and the shape was skewed left. The teacher decides to add 4 points to every students test score. What is the new mean, range, and shape for the distribution of test scores?

• mean=80, range = 20, shape is skewed left

• mean=76, range = 25, shape is skewed left

• mean=80, range = 25, shape is more skewed left

• mean=80, range = 20, shape is approx. symmetric

Multiple Choice

A 50 point test had a mean of 42 with a range of 25 points. The original shape of the distribution of test scores was approximately symmetric. The teacher decides to multiply all scores by 2 (so the total is out of 100). What is the new mean, range and shape for the distribution of test scores?

• mean=84, range = 50, approx. symmetric

• mean=84, range = 25, approx. symmetric

• mean=42, range = 25, approx. symmetric

• mean=84, range = 50, slightly skewed right

Poll

Can you:

LT1 - Describe the effect of adding or subtracting a constant on a distribution of quantitative data.

• Not at all

• With difficulty

• Somewhat

• Very Well

Poll

Can you:

LT2 - Describe the effect of multiplying or dividing by a constant on a distribution of quantitative data.

• Not at all

• With difficulty

• Somewhat

• Very Well

Poll

Can you:

LT3 - Analyze the effect of adding or subtracting a 

constant and multiplying or dividing by a constant 

on measures of center, location, and variability.

• Not at all

• With dificulty

• Somewhat

• Very Well