chapter 3

Question 1

percentiles

Answer 1

measures of central tendency that divide a group of data into 100 parts

Question 2

quartiles

Answer 2

measures of central tendency that divide a group of data into four subgroups or parts

Question 3

differences between mean, median, and mode

Answer 3

mean: can apply only to quantitative data
median: can apply to ordinal-level qualitative data and quantitative data
mode: can apply to nominal-level qualitative and quantitative data (can be bimodal and multimodal)

Question 4

advantages and disadvantages of mean

Answer 4

+ uses all the data and each data item influences the mean
- affected by outliers

Question 5

advantages and disadvantages of median

Answer 5

+ not affected by outliers
- not all info from the numbers is used; only considers the middle value

Question 6

advantages and disadvantages of mode

Answer 6

+ easy to determine
- data set my not have a mode

Question 7

Is the arithmetic mean greatly affected by any extreme value or values? Explain.

Answer 7

Yes, the mean is affected by extreme data values.Consider the mean salary of employees. A CEO or executive making over $500,000 in a company will increase the mean salary of employees and therefore a mean salary is not indicative of most of the employees’ salary.

Question 8

can you contrive a small set of data with no mode?

Answer 8

Any data set, regardless of size, with unique items in it will have no mode.

Question 9

frequency distribution

Answer 9

summary of data presented in the firm of class intervals and frequencies

Question 10

relative frequency

Answer 10

proportion of the total frequency that is in any given class interval in a frequency distribution

Question 11

range

Answer 11

difference between the largest value and smallest value of a data set

Question 12

is range affected by extreme values?

Answer 12

yes

Question 13

interquartile range

Answer 13

range of values between the first and third quartiles (q3 - q1)

Question 14

how to find deviations from the mean

Answer 14

each value minus the mean

Question 15

mean absolute deviation

Answer 15

average of the absolute values of the deviations around the mean for a set of numbers

Question 16

variance

Answer 16

the average of the squared deviations about the mean for a set of numbers

Question 17

standard deviation

Answer 17

square root of the variance

Question 18

empirical rule

Answer 18

used to state the approx percentage of values that lie within a given number of standard deviations from the mean of a set of approx normally distributed data (only used for 1o, 2o, and 3o)

Question 19

empirical rule percentages

Answer 19

1o - 68% of data within one standard deviation of mean
20 - 95% within 2 standard deviations
3o - 99.7% within three standard deviations

Question 20

chebyshev’s theorem

Answer 20

states that at least 1 - 1/k^2 values will fall within +/-k standard deviations of the mean regardless of the shape of the distribution

Question 21

z score

Answer 21

represents the number of standard deviations by which a value is above or below the mean of a set of numbers when the data are normally distributed

Question 22

coefficient of variation

Answer 22

the ratio of the standard deviation to the mean, expressed as a percentage, and is denoted CV

Question 23

Can the values for the range, the interquartile range, the variance, and the standard deviation ever be negative? Explain.

Answer 23

The range and IQR can be negative but not the variance and standard deviations because the deviations for the latter two are squared.

Question 24

What measure of variability can be used to compare variables when they have different units of measurement?

Answer 24

The coefficient of variation (denoted by CV) because it is based on the ratio, expressed as a percentage, of the standard deviation to the mean.Therefore, regardless of the unit of measure, comparisons may be made using the CV.

Question 25

skewness

Answer 25

when a distribution lacks symmetry

Question 26

skewed part is which part of the curve?

Answer 26

the long, thin part

Question 27

If the mode of a data set is smaller than the median, which in turn is smaller than the mean, the distribution of data is ____________ skewed.

Answer 27

positively

Question 28

On a certain day, the average closing share price of a group of stocks on the Toronto Stock Exchange is $35 (to the nearest dollar). If the median value is $33 and the mode is $21, is the distribution of these share prices skewed? If so, how?

Answer 28

skewed right