Chapter 3: Describing, Exploring, and Comparing Data

Question 1

Measure of Center

Answer 1

the value at the center or middle of a data set

Question 2

Arithmetic Mean (Mean)

Answer 2

the measure of center obtained by adding the values and dividing the total by the numbers of value. What most people call an average

Question 3

median

Answer 3

the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude

Question 4

Are median values affected by extreme values?

Answer 4

No, they are resistant measures of the center.

Question 5

How is the median found for a data set that has an odd number of values?

Answer 5

1. Sort the values 2. The median is the number located in the exact middle of the list.

Question 6

How is the median found for a data set that has an even number of values?

Answer 6

1. Sort the values 2. The median is found by computing the mean of the two middle numbers.

Question 7

mode

Answer 7

the value that occurs with the greatest frequency

Question 8

bimodal

Answer 8

two data values occur with the same greatest frequency

Question 9

multimodal

Answer 9

more than data values occur with the same greatest frequency

Question 10

no mode

Answer 10

no data value is repeated

Question 11

Which measure of central tendency can be used with nominal data.

Answer 11

Only mode

Question 12

midrange

Answer 12

the value midway between the maximum and minimum values in the original data set

Question 13

How is the midrange calculated?

Answer 13

(max value + min value)/2

Question 14

What is the range of a set of data values?

Answer 14

The difference between the max data value and the min data value.

Question 15

How is the range of a set of data values calculated?

Answer 15

range= (max value) - (min value)

Question 16

What is the standard deviation of a set of sample values?

Answer 16

A measure of how much data values deviate from the mean.

Question 17

Can the value of a standard deviation be negative?

Answer 17

NO!

Question 18

What units are standard deviations expressed in?

Answer 18

The units are the same as the units of the original data values.

Question 19

What is the range rule of thumb for understanding standard deviation?

Answer 19

For many data sets, the vast majority (such as 95%) of sample values lie within two standard deviations of the mean.

Question 20

How are “usual” values in a data set determined using the range rule of thumb?

Answer 20

(mean)+/-2*(standard deviation)

Question 21

Using the range rule of thumb, how are standard deviations roughly estimated from a collection of known samples?

Answer 21

range/4

Question 22

variance

Answer 22

a measure of variation equal to the square of the standard deviation

Question 23

Why is the sample variance s^2 an unbiased estimator of the population variance?

Answer 23

because the values of s^2 tend to target the value of population variance instead of systematically tending to overestimate or underestimate population variance.

Question 24

What is the empirical rule?

Answer 24

For data sets having a distribution that is approximately bell shaped, the following properties apply: ~68% of all values fall with in 1 standard deviation of the mean; ~95% of all values fall within 2 standard deviations of the mean; ~99.7% of all values fall within 3 standard deviations of the mean.

Question 25

What is Chebyshev's Theorem?

Answer 25

The proportion (or fraction) of any set of data lying within K standard deviations of the mean is always at least 1-1K^2, where K is any positive number greater than 1.

Question 26

Using Chebyshev's Theorem, what does K=2 mean?

Answer 26

At least 3/4 (or 75%) of all values lie within 2 standard deviations of the mean.

Question 27

Using Chebyshev's Theorem, what does K=3 mean?

Answer 27

At least 8/9 (or 89%) of all values lie within 3 standard deviations of the mean.

Question 28

variance

Answer 28

a measure of variation equal to the square of the standard deviation

Question 29

Why is the sample variance s^2 an unbiased estimator of the population variance?

Answer 29

because the values of s^2 tend to target the value of population variance instead of systematically tending to overestimate or underestimate population variance.

Question 30

What is the empirical rule?

Answer 30

For data sets having a distribution that is approximately bell shaped, the following properties apply: ~68% of all values fall with in 1 standard deviation of the mean; ~95% of all values fall within 2 standard deviations of the mean; ~99.7% of all values fall within 3 standard deviations of the mean.

Question 31

What is Chebyshev's Theorem?

Answer 31

The proportion (or fraction) of any set of data lying within K standard deviations of the mean is always at least 1-1K^2, where K is any positive number greater than 1.

Question 32

Using Chebyshev's Theorem, what does K=2 mean?

Answer 32

At least 3/4 (or 75%) of all values lie within 2 standard deviations of the mean.

Question 33

Using Chebyshev's Theorem, what does K=3 mean?

Answer 33

At least 8/9 (or 89%) of all values lie within 3 standard deviations of the mean.

Question 34

What is the coefficient of variation?

Answer 34

For a set of nonnegative sample or population data, expressed as percent, CV describes the standard deviation relative to the mean.

Question 35

How is the coefficient of variation calculated?

Answer 35

cv= (standard deviation/the mean) *100

Question 36

What are measures of relative standing?

Answer 36

Numbers showing the location of data values relative to the other values within a data set.

Question 37

In which ways are measures of relative standing used?

Answer 37

To compare values from different data sets or to compare values within the same data set.

Question 38

Name 4 examples of measures of relative standing.

Answer 38

z scores, percentiles, quartiles, and boxplots

Question 39

What is a z score?

Answer 39

The number of standard deviations that a given value x is above or below the mean.

Question 40

How are z scores determined?

Answer 40

z= (x-the mean)/standard deviation; round score to 2 decimal places

Question 41

Whenever a value is less than the mean, is its z-score positive or negative?

Answer 41

Negative

Question 42

What are ordinary z-score values?

Answer 42

-2<=2

Question 43

What are unusual z-score values?

Answer 43

zscore< -2 or zscore>2

Question 44

What are percentiles?

Answer 44

Measures of location that divide a set of data into 100 groups with about 1% of the values in each group.

Question 45

How is the percentile of a data value found?

Answer 45

(# of values less than x/ total # of values) *100

Question 46

How is a percentile converted to a data value?

Answer 46

L=(k/100)*n, where n=total number of values in the data set, k=percentile being used, L=locator that gives position of a value, Pk= kth percentile

Question 47

How is Pk found with a "L" value that is a whole number?

Answer 47

By adding the Lth value and the next value and dividing the total by 2.

Question 48

How is Pk found with a "L" value that is not a whole number?

Answer 48

By rounding L up to the next larger whole number.

Question 49

What are quartiles?

Answer 49

Measures of location, denoted Q1, Q2, and Q3, which divide a set of data into 4 equal parts with about 25% of the values in each group.

Question 50

Q1

Answer 50

separates the bottom 25% of sorted values from the top 75%

Question 51

Q2

Answer 51

same as the median; separates the bottom 50% of sorted values from the top 50%

Question 52

Q3

Answer 52

separates the bottom 75% of sorted values from the top 25%

Question 53

What is a interquartile range (IQR)?

Answer 53

Q3-Q1

Question 54

What is a semi-interquartile range?

Answer 54

(Q3-Q1)/2

Question 55

What is a midquartile?

Answer 55

(Q3+Q1)/2

Question 56

How is the 10-90 percentile range determined?

Answer 56

P90-P10

Question 57

What is a boxplot?

Answer 57

A graph of a data set that consists of a line extending from the minimum value to the maximum value, and a box with lines drawn at Q1, the median, and Q3.