Chapter 3 Section 2: Measure Of Dispersion

Question 1

Standard deviation

Answer 1

A measure of how much we might expect a typical member of the data set to differ from the mean

Question 2

Coefficient of variation

Answer 2

The ratio of the standard deviation to the mean as a percentage; allows comparison of the spreads of data from different sources, regardless of differences in units of measurement

Question 3

Variance

Answer 3

The square of the standard deviation

Question 4

Empirical rule

Answer 4

Used with the bell-shaped distributions of data to estimate the percentage of values within the standard deviations of the mean

Question 5

Chebyshev’s theorem

Answer 5

Gives a minimum estimate of the percentage of data within a few a standard deviations of the mean for any distribution

Question 6

Range

Answer 6

Largest data value in a data set - smallest data value in a data set

Question 7

Properties of the range

Answer 7

1) easiest measure of dispersion to calculate

2) only affected by the largest and smallest values in the data set , so it can be misleading

Question 8

Population standard deviation

Answer 8

Theta symbol

Question 9

Sample standard deviation

Answer 9

S

Question 10

Properties of standard deviation

Answer 10

1) easily computed using a calculator or computer
2) affected by every value in the data set
3) population standard deviation and sample standard deviation formulas yield different results
4) interpreted as the average distance a data value is from the mean; thus it cannot take on negative values
5) same units as the units of the data
6) larger standard deviation indicated that data values are more spread out, smaller standard deviation indicated that data values lie closer together
7) if it equals 0 then all of the data values are equal to the mean
8) equal to the square root of the variance

Question 11

Population/ sample variance

Answer 11

Standard deviation squared

Question 12

Properties of variance

Answer 12

1) easily computed using a calculator or computer
2) affected by every value in the data set
3) population variance and sample variance formulas yield different results
4) difficult to interpret because of its unusual squared units
5) equal to the square of the standard deviation
6) preferred over the standard deviation in many statistical tests because of its simpler formula

Question 13

Empirical rule for bell-shaped distributions

Answer 13

Approx 68% of data values lie within one standard deviation of the mean
Approx 95% of data values lie within two standard deviations of the mean
Approx 99.7% of data values lie within three standard deviations of the mean

Question 14

Chebychev’s theorem

Answer 14

K=number of classes
When k=2 75% of the data lie within 2 standard deviations of the mean
When k=3 88.9% of the data lie within 3 standard deviations of the mean