Chapter 2: Describing Quantitative Distributions With Numbers

Question 1

What is a parameter?

Answer 1

A number that describes the population.

Question 2

What is a statistic?

Answer 2

A number that can be computed from the sample data without making use of any unknown parameters; a number that describes a sample.

Question 3

True or False?: Statistics are often used to describe parameters.

Answer 3

True

Question 4

What is the median?

Answer 4

The midpoint of a distribution; the number such that half the observations are smaller and the other half are larger.

Question 5

How do you find the median?

Answer 5

1. Arrange all observations from smallest to largest.
2. Find the median by calculating (n+1)/2, then count up from the smallest observation this many times.

Question 6

What is a percentile?

Answer 6

The value such that some percent (p) of observations in a distribution lie below it is called the pth percentile.

Question 7

What is another term to describe the 50th percentile?

Answer 7

Median.

Question 8

What is a resistant measure?

Answer 8

A measure of any aspect of a distribution that is relatively unaffected by changes in the numerical value of a small proportion of the total number of observations.

Question 9

Is mean a resistant measure?

Answer 9

No.

Question 10

Is median a resistant measure?

Answer 10

Yes.

Question 11

Why is median usually reported rather than the mean for skewed distributions?

Answer 11

Because the mean is sensitive to extremities or outliers.

Question 12

What is the range?

Answer 12

The distance between a distribution’s largest and smallest values.

Question 13

What is the interquartile range (IQR) and how is it calculated?

Answer 13

The distance between the first and third quartiles; Q3-Q1.

Question 14

What is the first quartile (Q1)?

Answer 14

The value larger than 25% of the distribution’s values.

Question 15

What is the second quartile (Q2)?

Answer 15

The value larger than 50% of the distribution’s values.

Question 16

What is the third quartile (Q3)?

Answer 16

The value larger than 75% of the distribution’s values.

Question 17

How do you calculate Q1?

Answer 17

Take the median of the observations that are positioned to the left of the overall median (do not include the value of the overall median).

Question 18

How do you calculate Q2?

Answer 18

Take the median of the observations that are positioned to the right of the overall median (do not include the value of the overall median).

Question 19

What does the five number summary include?

Answer 19

The distribution’s minimum, Q1, Q2, Q3, and maximum.

Question 20

What is the most common numerical description of a distribution?

Answer 20

Mean and standard deviation.

Question 21

What is variance (s^2)?

Answer 21

The measure of spread about the mean of a distribution; standard deviation squared.

Question 22

What does variance tell you?

Answer 22

How much the data varies from the mean.

Question 23

What are the degrees of freedom?

Answer 23

n-1

Question 24

If mean is not used as a measure of center, should standard deviation be used as a measure of spread?

Answer 24

No. Standard deviation measures spread about the mean and should only be used when the mean is also being used/reported.

Question 25

When does s=0?

Answer 25

When there is no spread.

Question 26

When is s<0?

Answer 26

Never. s is always greater than or equal to 0.

Question 27

True or False?: Standard deviation is a resistant measure of spread.

Answer 27

False. Standard deviation is not a resistant measure.

Question 28

What type of graph displays the five number summary?

Answer 28

A boxplot.

Question 29

True or False?: A boxplot shows less detail than a histogram, but more detail than a dotplot.

Answer 29

False. A boxplot shows less detail than both a dotplot and a histogram.

Question 30

In a box plot, when is Q1 and Q3 equally distant from the median?

Answer 30

When the distribution is symmetric.

Question 31

In a box plot, when is Q1 further from the median than Q3?

Answer 31

When the distribution is skewed to the left.

Question 32

In a box plot, when is Q3 further from the median than Q1?

Answer 32

When the distribution is skewed to the right.

Question 33

How does the IQR rule define suspected outliers?

Answer 33

Per the IQR rule, a value is determined to be a suspected outlier if it falls more than 1.5IQR above Q3 or more than 1.5IQR below Q1.

Question 34

True or false?: If a value is determined a suspected outlier by the IQR rule, it should always be considered an outlier.

Answer 34

False. A value considered a suspected outlier by the IQR rule should not be considered an outlier if it still follows the pattern of the distribution.

Question 35

What are the three possible reasons for outliers in data?

Answer 35

Human error in experimentation or data collection, human error in recording information, and the unexplainable.

Question 36

What are the steps one should take to organize a statistical problem?

Answer 36

1. State - state what the practical question is in context of the real world setting. 2. Plan - Plan what specific statistical operations are necessary for the problem. 3. Solve - analyze the data with graphs and computations suitable for the problem. 4. Conclude - give a practical conclusion in the setting of the real world problem.

Question 37

What numerical summaries are suitable for a symmetric distribution?

Answer 37

Mean and standard deviation.

Question 38

What numerical summaries are suitable for a non-symmetric distribution?

Answer 38

The five number summary.

Question 39

True or false?: True parameters can never be found.

Answer 39

True.

Question 40

Why is a boxplot advantageous?

Answer 40

A boxplot displays the information gained from a bar graph but in more detail.

Question 41

How is measurement of spread displayed on a bar graph?

Answer 41

Through an error bar.

Question 42

What does an error bar usually display, specifically?

Answer 42

Standard deviation.