2.4-2.8

Question 1

What does knowledge of a data set’s variability and center help us to do?

Answer 1

can help us visualize the shape of the data set as well as its extreme values.

Question 2

What is the range?

Answer 2

The range of a quantitative data set is equal to the largest measurement minus the smallest measurement.

Question 3

What is a con of range? Why is this a con?

Answer 3

a rather insensitive measure of data variation when the data sets are large. This is because two data sets can have the same range and be vastly different with respect to data variation.

Question 4

What is sample variance?

Answer 4

The sample variance for a sample of n measurements is equal to the sum of the squared deviations from the mean, divided by . The symbol s^2 is used to represent the sample variance.

Question 5

What does it mean if the deviations are mostly small?

Answer 5

he data are clustered around the mean, x

, and therefore do not exhibit much variability.

Question 6

What is the sample standard deviation?

Answer 6

The sample standard deviation, s, is defined as the positive square root of the sample variance

Question 7

What symbol represents a population variance?

Answer 7

sigma

Question 8

Why do we use n-1 when calculating sample variance instead of just n?

Answer 8

n tends to produce an underestimate of sigma^2.

Question 9

What does the value of standard deviation indicate?

Answer 9

The larger the standard deviation, the more variable the data are. The smaller the standard deviation, the less variation there is in the data.

Question 10

What is Chebyshev’s rule?

Answer 10

a. It is possible that very few of the measurements will fall within one standard deviation of the mean
b. At least 3/4 of the measurements will fall within two standard deviations of the mean
c. At least 8/9 of the measurements will fall within three standard deviations of the mean
d. Generally, for any number k greater than 1, at least (1-1/k^2) of the measurements will fall within k standard deviations of the mean (x-ks, x+ks)

Question 11

What is the empirical rule?

Answer 11

a. Approximately 68% of the measurements will fall within one standard deviation of the mean
b. Approximately 95% of the measurements will fall within two standard deviations of the mean
c. Approximately 99.7% (essentially all) of the measurements will fall within three standard deviations of the mean

Question 12

What sets of data do Chebyshev’s rule and the empirical rule apply to?

Answer 12

CR: any
EMP: mound-shaped

Question 13

WHat are measures of relative standing?

Answer 13

Descriptive measures of the relationship of a measurement to the rest of the data

Question 14

What is the pth percentile?

Answer 14

For any set of n measurements (arranged in ascending or descending order), the pth percentile is a number such that p% of the measurements fall below that number and (100-p)% fall above it.

Question 15

Explain the quartiles/

Answer 15

The lower quartile (QL) is the 25th percentile of a data set. The middle quartile (M) is the median or 50th percentile. The upper quartile (QU) is the 75th percentile.

Question 16

What is a z score for measurement x? WHat does it represent?

Answer 16

z = (x-x)/sb
The final result, the z-score, represents the distance between a given measurement x and the mean, expressed in standard deviations.

Question 17

What does a large, small and zero/near zero z-score indicate?

Answer 17

A large positive z-score implies that the measurement is larger than almost all other measurements, whereas a large negative z-score indicates that the measurement is smaller than almost every other measurement. If a z-score is 0 or near 0, the measurement is located at or near the mean of the sample or population.

Question 18

What are expectations of z-scores for mound-shaped data?

Answer 18

Approximately 68% of the measurements will have a z-score between -1 and 1.

Approximately 95% of the measurements will have a z-score between -2 and 2.

Approximately 99.7% (almost all) of the measurements will have a z-score between -3 and 3.

Question 19

What is an outlier?

Answer 19

An observation that is unusually large or small relative to the data values we want to describe

Question 20

When do outliers most often occur?

Answer 20

The measurement is observed, recorded, or entered into the computer incorrectly.
The measurement comes from a different population.
The measurement is correct but represents a rare (chance) event

Question 21

What is the interquartile range?

Answer 21

The interquartile range (IQR) is the distance between the lower and upper quartiles:

Question 22

Describe a box plot.

Answer 22

A rectangle (the box) is drawn with the ends (the hinges) drawn at the lower and upper quartiles. The median M of the data is shown in the box, usually by a line or a symbol (such as “ +”).

Question 23

What are the inner fences? What are the whiskers? in a box plot.

Answer 23

The points at distances 1.5(IQR) from each hinge mark the inner fences of the data set. Lines (the whiskers) are drawn from each hinge to the most extreme measurement inside the inner fence.

Question 24

What are the outer fences?

Answer 24

A second pair of fences, the outer fences, appears at a distance of 3(IQR) from the hinges. One symbol (e.g., “*”) is used to represent measurements falling between the inner and outer fences, and another (e.g., “0”) is used to represent measurements that lie beyond the outer fences. Thus, outer fences are not shown unless one or more measurements lie beyond them.

Question 25

What does the line inside the box in a box plot represent?

Answer 25

Center of the distribution

Question 26

What does it mean if one whisker is longer than the other in a box ploy?

Answer 26

Data is probably skewed in the direction of the longer whisker.

Question 27

How much of the total measurements should fall beyond the inner fences?

Answer 27

Less than 5%.

Question 28

What should you do before removing an outlier from the data set?

Answer 28

Before removing the outliers from the data set, a good analyst will make a concerted effort to find the cause of the outliers

Question 29

What is a rule of thumb for detecting outliers in box plots?

Answer 29

Observations falling between the inner and outer fences are deemed suspect outliers. Observations falling beyond the outer fence are deemed highly suspect outliers.

Question 30

What is a rule of thumb for detecting outliers in a z-score?

Answer 30

Observations with z-scores greater than 3 in absolute value are considered outliers. For some highly skewed data sets, observations with z-scores greater than 2 in absolute value may be outliers.

Question 31

What is a bivariate relationship?

Answer 31

relationship between two quantitative variables

Question 32

What is a way to describe a bivariate relationship?

Answer 32

Scatterplot.

Question 33

What does it mean if variables are positively correlated? Negatively?

Answer 33

When an increase in one variable is generally associated with an increase in the second variable, we say that the two variables are “positively related” or ­“positively correlated.
if one variable has a tendency to decrease as the other increases, we say the variables are “negatively correlated.

Question 34

Can a measure of reliability be attached to inferences made about bivariate relationships based on scatterplots of sample data?

Answer 34

No.

Question 35

Explain the difference between a bar graph and a histogram.

Answer 35

Bar graph is used to describe qualitative data, histogram is for quantitative data. Therefore, the x-axis
of bar graph can be anything (categories name) while x-axis of histogram can only be numerical values.
The columns in bar graph do not touch each other, but histogram column can.

Question 36

give the shortcut to determine variance

Answer 36