Chapter 3

Question 1

3 main “measures of center”

Answer 1

1. Mean
2. Median
3. Mode

Question 2

Mean

Answer 2

Obtained by dividing the sum of all values by the number of values in the data set.

Question 3

Median

Answer 3

The value that divides a data set that has been sorted in increasing order into two equal halves.

Question 4

Mode

Answer 4

The value that occurs w/ the highest frequency in a data set.

Question 5

Mean for population data

Answer 5

u = sum on all x’s / N

Question 6

Mean for sample data

Answer 6

X bar = sum of all x’s /n

Question 7

2 steps to calculate the median

Answer 7

1. Sort the data set into increasing order
2. Find the value that divides the sorted data set in two equal parts.

Question 8

Can there be no mode?

Answer 8

Yes

Question 9

Can modes be from qualitative data?

Answer 9

Yes

Question 10

Can there be more than one mode?

Answer 10

Yes

Question 11

What are the mean, median, and mode of a symmetrical histogram /distribution curve

Answer 11

Mean = median = mode

Question 12

Mean, median, and mode of a right-skewed histogram

Answer 12

Mean > median > mode

Question 13

Left-skewed histogram mean, median, and mode

Answer 13

Mean < median < mode

Question 14

Trimmed mean

Answer 14

After we drop K% of the values from each end of a ranked data set, the mean of the remaining values is called the K% trimmed mean.

Question 15

Weighted mean

Answer 15

When each value of a data set is assigned a different weight.
Sum of x* W/ sum of W

Question 16

Measures of dispersion tell us…

Answer 16

How much variation exists around that “typical value”

Question 17

3 main measures of dispersion

Answer 17

1. Range
2. Variance
3. Standard deviation

Question 18

Range

Answer 18

The difference between the largest value and the smallest value.

Question 19

Variance

Answer 19

A measure of how much the values in a dataset differ from the mean.

Question 20

Standard deviation

Answer 20

A measure of the average distance of each data point from the mean. The square root of variance

Question 21

Range formula

Answer 21

Largest value - smallest value

Question 22

Disadvantages of range

Answer 22

1. Only based on 2 values
   2, affected by outliers

Question 23

Can the variance and the standard deviation be negative?

Answer 23

No

Question 24

Units for standard deviation

Answer 24

Same as the original units

Question 25

Units for variation

Answer 25

The square of the original data's units

Question 26

Coefficient of variation ( CV )

Answer 26

A measure of relative variability. Useful if you are comparing the variation of two datasets w/ different magnitudes of value.

Question 27

Variance and SD depend on...

Answer 27

The units of measurement

Question 28

Coefficient of variation units

Answer 28

Expressed as a percentage of the mean. Has no units and is always expressed as a percentage.

Question 29

Coefficient of variation formula

Answer 29

100 x SD / mean

Question 30

Mean of grouped data for population data

Answer 30

u = sum of frequency x midpoint /n

Question 31

Mean of grouped data for sample data

Answer 31

X bar = sum of frequency x midpoint /n

Question 32

Standard deviation

Answer 32

A measure of the average distance of each data point from the mean.

Question 33

ChebyShev's theorem

Answer 33

For any number k greater than 1, at least ( 1-1 / k^2 ) of the data values lie within K standard deviations of the mean

Question 34

ChebyShey's theorem works for...

Answer 34

Any distribution shape

Question 35

Empirical rule

Answer 35

If our distribution is a "bell-shaped"or “normal" or "Gaussian" we use the empirical rule. 68% of observations lie w/ in one standard deviation of the mean 95% of the observations lie with in 2 SDs of the mean 99. 7% of the observations lie with in 3 SDs of the mean

Question 36

Quartile

Answer 36

Three summary measures ( Q1, Q2, Q3 ) that divide a ranked data set into four equal parts. Q2 is the same as the median. Splits the data into 4 sections. (Each contains 25% of the observations of a data set)

Question 37

Interquartile range (irq)

Answer 37

The difference between Q3 and Q 1 IRQ = Q3 - Q1 Another measure of dispersion. Small IRQ = less spread out data Large IRQ = more spread out data

Question 38

Percentiles

Answer 38

99 summary measures that divide a ranked data set into 100 equal parts. Each portion contains 1% of the observations of a data set.

Question 39

The (approximate) value of the K Th percentile is sample of size N is:

Answer 39

Pk = value of the ( kn / 100 ) Th term in a ranked data set Always round the position up.

Question 40

Given a certain number in a set and find its percentile.

Answer 40

Percentile = number of values less than k / total number of values in the data set X 100%

Question 41

Box-and-whisker plot

Answer 41

Shows 5 measures: 1. Median 2.Q1 3. Q3 4. Minimum 5. Maximum Lower inner fence = Q1 - 1.5x IQR Upper inner fence = Q3 + 1.5x1QR Outliers are plotted outside the fences.