Chapter 5

Question 1

What are the three features of distributions?

Answer 1

Shape, Centre and Width

Question 2

Variation

Answer 2

The width of a distribution; how much values of a variable differ from one another

Question 3

Measures of variation

Answer 3

The measures of variation convey something about how wide a distribution is; how far it is from the smallest point to the largest point, how far it is from the mean to a representative point etc. Sometimes called measures of variability or dispersion. There are three measures of variation: range, the standard deviation, variance.

Question 4

What are the three measures of variation?

Answer 4

Range, the standard deviation, variance.

Question 5

Range

Answer 5

A measure of the width of a distribution equal to the highest value minus the lowest value (the distance from the lowest point from the highest point).

Question 6

Deviation

Answer 6

The “distance” any one point is from the mean.

Question 7

What is the mean of deviations?

Answer 7

Deviations always sum to zero. Therefore the mean of the deviations is always zero.

Question 8

Variance

Answer 8

A measure of the width of a distribution equal to the mean of the squared deviations.

Question 9

Finish this sentence… when the distributions are wide, the deviations are…

Answer 9

Big

Question 10

Finish this sentence… when the distrubutions are wide, the squared deviations are…

Answer 10

Big and the average of the squared deviations are not zero - in fact, the wider the distribution, the bigger the average of the squared deviations.

Question 11

Standard deviation

Answer 11

A measure of the width of a distribution equal to the square root of the mean of the squared deviations; it is the square root of the variance.

Question 12

What is the formula for the variance?

Answer 12

You compute the variance by adding the squared deviations and dividing by the number of deviations.

Question 13

What do we call the variance of a population?

Answer 13

o2 (sigma squared)

Question 14

Sum of squares

Answer 14

The sum of the squared deviations

Question 15

Inflection point

Answer 15

The point on a graph curve where the curvature changes from upward to downward or from downward to upward

Question 16

How many inflection points does a normal distribution have?

Answer 16

2 inflection points

Question 17

What is the distance from the mean to an inflection point on every normal distribution?

Answer 17

1 standard deviation

Question 18

What are the two methods for eyeball-estimating the standard deviation?

Answer 18

1. The inflection point method (begins with a graphical frequency distribution)
2. The range method (used with data presented in a table)

Question 19

What is the inflection point method for eyeball-estimating the standard deviation?

Answer 19

The procedure is to super-impose as best you can a normal distribution that reflects the shape of the histogram or frequency polygon.

Question 20

What are the steps to the inflection point method for eyeball-estimating the standard deviation?

Answer 20

1. Display the data as a histogram or frequency polygon.
2. Superimpose a normal distribution on the histogram.
3. Locate the inflection points and draw an arrow between one of the inflection points and the mean. That arrow indicates the standard deviation.
4. With your imagination, grab that arrow and slide it down to a convenient place on the x-axis to measure it.

Question 21

What is the range method for eyeball-estimating the standard deviation?

Answer 21

The standard deviation is roughly a quarter of the range.

Question 22

If you have a histogram which eyeball-estimating method for the standard deviation should you use?

Answer 22

The inflection point method.

Question 23

What are the steps to the range method for eyeball-estimating the standard deviation?

Answer 23

1. Scan the data for the lowest and highest levels.
2. Subtract the lowest value from the highest value to obtain the range.
3. Divide the range by 4.

Question 24

If we take the sample size into account, what are the refined steps of eyeball-estimating the standard deviation?

Answer 24

If the sample size is smaller than 13 , then a better approximation of the standard deviation is one-third or one half of the range. If the sample size is larger than 30, then a better approximation is one-fifth or one-sixth of the range.

Question 25

What is the definition of standard deviation?

Answer 25

a quantity expressing by how much the members of a group differ from the mean value for the group.