Statistics, parameters

"Samples produce____________, populations produce _________"

Mean

Which of the following provides a measure of central location for the data?

Sample statistic

A numerical value used as a summary measure for a sample, such as sample mean, is known as

Can be smaller, larger, or equal to the population parameter

Since the population size is always larger than the sample size, then the sample statistic

A. Can never be larger than the population parameter

B. Can never be equal to the population parameter

C. Can be smaller, larger, or equal to the population parameter

D. Can never be smaller than the population parameter

A. Can never be larger than the population parameter

B. Can never be equal to the population parameter

C. Can be smaller, larger, or equal to the population parameter

D. Can never be smaller than the population parameter

Population Parameter

μ

0.30%

The hourly wages of a sample of 130 system analysts are given below

mean=60

mode=73

median=74

range=20

variance=324

The coefficient of variation equals...?

mean=60

mode=73

median=74

range=20

variance=324

The coefficient of variation equals...?

24

The variance of a sample of 169 observations equals 576. The standard deviation of the sample equals..?

50th percentile

The median of a sample will always equal the

central location

the median is a measure of

third quartile

the 75th percentile is referred to as the

less than or equal to this value

the "p"th percentile is a value such that at least p percent of the observations are

A. Less than or equal to this value

B. Less than this value

C. More than or equal to this value

D. More than this value

A. Less than or equal to this value

B. Less than this value

C. More than or equal to this value

D. More than this value

Range

The difference between the largest and the smallest data values are

The First Quartile

the same as the 25th percentile

Variance

Which of the following is not a measure of central location?

A. Mean

B. Median

C. Variance

D. Mode

A. Mean

B. Median

C. Variance

D. Mode

The average value of the two middle items when all items are arranged in ascending order

If a data set has an even number of observations, the median

A. Cannot be determined

B. Is the average value of the two middle terms

C. Must be equal to the mean

D. Is the average value of the two middle items when all items are arranged in ascending order

A. Cannot be determined

B. Is the average value of the two middle terms

C. Must be equal to the mean

D. Is the average value of the two middle items when all items are arranged in ascending order

Interquartile Range

Which of the following is a measure of dispersion?

A. Percentiles

B. Quartiles

C. Interquartile Range

D. All of the above are measures of dispersion

A. Percentiles

B. Quartiles

C. Interquartile Range

D. All of the above are measures of dispersion

Mode

The most frequently occurring value of a data set is called the

Interquartile Range

the difference between the third quartile and the first quartile

Rounded up

If index "i" (which is used to determine the location of the "p"th) is not an integer, its value should be

A. squared

B. divided by (n-1)

C. rounded down

D. rounded up

A. squared

B. divided by (n-1)

C. rounded down

D. rounded up

Positive

When the data are skewed to the right, the measure of skewness will be

A. negative

B. zero

C. positive

D. one

A. negative

B. zero

C. positive

D. one

Greater than the median

When data are positively skewed, the mean will usually be

A. greater than the median

B. smaller than the median

C. equal to the median

D. positive

A. greater than the median

B. smaller than the median

C. equal to the median

D. positive

50th Percentile

Which of the following is not a measure of dispersion?

A. the range

B. the 50th percentile

C. the standard deviation

D. the interquartile range

A. the range

B. the 50th percentile

C. the standard deviation

D. the interquartile range

the range is influenced too much by extreme values

The interquartile range is used as a measure of variability to overcome what difficulty of the range?

A. the sum of the range variances is zero

B. the range is difficult to compute

C. the range is influenced too much by extreme values

D. the range is negative

A. the sum of the range variances is zero

B. the range is difficult to compute

C. the range is influenced too much by extreme values

D. the range is negative

the data set is a sample

If the variance of a data set is correctly computed with the formula using (n-1) in the denominator, which of the following is true?

A. the data set is a sample

B. the data set is a population

C. the data set could be either a sample or a population

D. the data set is from a census

A. the data set is a sample

B. the data set is a population

C. the data set could be either a sample or a population

D. the data set is from a census

data values are treated as if they occur at the midpoint of a class

In computing descriptive statistics from grouped data (like a frequency histogram),

A. data values are treated as if they occur at the midpoint of a class

B. the grouped data result is more accurate than the ungrouped result

C. the grouped data computations are used only when a population is being analyzed

D. None of these alternatives is correct

A. data values are treated as if they occur at the midpoint of a class

B. the grouped data result is more accurate than the ungrouped result

C. the grouped data computations are used only when a population is being analyzed

D. None of these alternatives is correct

range

The measure of dispersion that is influenced most by extreme values is

A. variance

B. standard deviation

C. range

D. interquartile range

A. variance

B. standard deviation

C. range

D. interquartile range

only when individual data values are unavailable

When should measures of location and dispersion be computed from grouped data rather than from individual data values?

A. as much as possible since computations are easier

B. only when individual data values are unavailable

C. whenever computer packages from descriptive statistics are unavailable

D. only when the data are from a population

A. as much as possible since computations are easier

B. only when individual data values are unavailable

C. whenever computer packages from descriptive statistics are unavailable

D. only when the data are from a population

standard deviation

The descriptive measure of dispersion that is based on the concept of a deviation about the mean is

A. range

B. interquartile range

C. absolute value of the range

D. standard deviation

A. range

B. interquartile range

C. absolute value of the range

D. standard deviation

mean

The measure of location which is the most likely to be influenced by extreme values in the data set is the

A. range

B. median

C. mode

D. mean

A. range

B. median

C. mode

D. mean

mean

The most important statistical descriptive measure of the location of a data set is the

A. mean

B. median

C. mode

D. variance

A. mean

B. median

C. mode

D. variance

Negative

The numerical value of the standard deviation can never be

A. larger than the variance

B. zero

C. negative

D. smaller than the variance

A. larger than the variance

B. zero

C. negative

D. smaller than the variance

Sample Variance

Could be smaller, equal to, or larger than the true value of the population variance

Negative

The variance can never be

A. Zero

B. Larger than the standard deviation

C. Negative

D. Smaller than the standard deviation

A. Zero

B. Larger than the standard deviation

C. Negative

D. Smaller than the standard deviation

None of these alternatives is correct

If two groups of numbers have the same mean, then

A. their standard deviations must also be equal

B. their medians must also be equal

C. their modes must also be equal

D. None of these alternatives is correct

A. their standard deviations must also be equal

B. their medians must also be equal

C. their modes must also be equal

D. None of these alternatives is correct

Always equal to zero

The sum of deviations of the individual data elements from their mean is

A. always greater than zero

B. always less than zero

C. sometimes greater than and sometimes less than zero, depending on the data elements

D. always equal to zero

A. always greater than zero

B. always less than zero

C. sometimes greater than and sometimes less than zero, depending on the data elements

D. always equal to zero

standard deviation of the population

σ

mean of the population

μ

variance of the population

σ²

size of the population

N

mean of the sample

x̅

size of the sample

n

Covariance

A numerical measure of linear association between two variables is the

Positive relation between the independent and the dependent variables

Positive values of covariance indicate

A. a positive variance of the x values

B. a positive variance of the y values

C. the standard deviation is positive

D. positive relation between the independent and the dependent variables

A. a positive variance of the x values

B. a positive variance of the y values

C. the standard deviation is positive

D. positive relation between the independent and the dependent variables

Correlation Coefficient

A numerical measure of linear association between two variables

-1 and +1

The coefficient of correlation ranges between

A. 0 and 1

B. -1 and +1

C. minus infinity and plus infinity

D. 1 and 100

A. 0 and 1

B. -1 and +1

C. minus infinity and plus infinity

D. 1 and 100

Cannot be larger than 1

The coefficient of correlation

A. is the same as the coefficient of determination

B. can be larger than 1

C. cannot be larger than 1

D. cannot be negative

A. is the same as the coefficient of determination

B. can be larger than 1

C. cannot be larger than 1

D. cannot be negative

the trimmed mean

When the smallest and largest percentage of times are removed from a data set and the mean is computed, the mean of the remaining is

A. the median

B. the mode

C. the trimmed mean

D. any of the above

A. the median

B. the mode

C. the trimmed mean

D. any of the above

Must be at least zero

During a cold weather, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperature of the ten day period

A. is negative since all the numbers are negative

B. must be at least zero

C. cannot be computer since all the numbers are negative

D. can be either negative or positive

A. is negative since all the numbers are negative

B. must be at least zero

C. cannot be computer since all the numbers are negative

D. can be either negative or positive

Mode

Which of the following is not a measure of dispersion?

A. mode

B. standard deviation

C. range

D. interquartile range

A. mode

B. standard deviation

C. range

D. interquartile range

None of these alternatives is correct

Since the mode is the most frequently occurring data value, it

A. can never be larger than the mean

B. is always larger than the median

C. is always larger than the mean

D. none of these alternatives is correct

A. can never be larger than the mean

B. is always larger than the median

C. is always larger than the mean

D. none of these alternatives is correct

6

A researcher has collected the following sample data:

5

6

12

7

6

5

8

12

5

4

The median is...?

5

6

12

7

6

5

8

12

5

4

The median is...?

5

A researcher has collected the following sample data:

5

6

12

7

6

5

8

12

5

4

The mode is...?

5

6

12

7

6

5

8

12

5

4

The mode is...?

7

A researcher has collected the following sample data:

5

6

12

7

6

5

8

12

5

4

The mean is...?

5

6

12

7

6

5

8

12

5

4

The mean is...?

8

A researcher has collected the following sample data:

5

6

12

7

6

5

8

12

5

4

The 75th percentile is...?

5

6

12

7

6

5

8

12

5

4

The 75th percentile is...?

16.5

A researcher has collected the following 5 data points:

3

5

12

3

2

The variance is...?

3

5

12

3

2

The variance is...?

4.062

A researcher has collected the following 5 data points:

3

5

12

3

2

The standard deviation is...?

3

5

12

3

2

The standard deviation is...?

81.24%

A researcher has collected the following 5 data points:

3

5

12

3

2

The coefficient of variation is...?

3

5

12

3

2

The coefficient of variation is...?

10

A researcher has collected the following 5 data points:

3

5

12

3

2

The range is...?

3

5

12

3

2

The range is...?

6

A researcher has collected the following 5 data points:

3

5

12

3

2

The interquartile range is...?

3

5

12

3

2

The interquartile range is...?

67

The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway.

Speed (mph) Frequency

50-54 2

55-59 4

60-64 5

65-69 10

70-74 9

75-79 5

----

35

The mean is...?

Speed (mph) Frequency

50-54 2

55-59 4

60-64 5

65-69 10

70-74 9

75-79 5

----

35

The mean is...?

50

The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway.

Speed (mph) Frequency

50-54 2

55-59 4

60-64 5

65-69 10

70-74 9

75-79 5

----

35

The variance is...?

Speed (mph) Frequency

50-54 2

55-59 4

60-64 5

65-69 10

70-74 9

75-79 5

----

35

The variance is...?

7.071

The following is the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway.

Speed (mph) Frequency

50-54 2

55-59 4

60-64 5

65-69 10

70-74 9

75-79 5

----

35

The standard deviation is...?

Speed (mph) Frequency

50-54 2

55-59 4

60-64 5

65-69 10

70-74 9

75-79 5

----

35

The standard deviation is...?

Decrease

The average age of students at KSU increased from 22 with a standard deviation of 3.96 to an average age of 24 with a standard deviation of 4.08. The relative dispersion around the mean

A. Decrease

B. Increase

C. Stayed the same

D. Disappeared

A. Decrease

B. Increase

C. Stayed the same

D. Disappeared

19.286

The following observations are given for two variables:

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the sample covariance...?

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the sample covariance...?

6.32

The following observations are given for two variables:

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the standard deviation for x?

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the standard deviation for x?

8.83

The following observations are given for two variables:

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the standard deviation for y?

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the standard deviation for y?

0.345

The following observations are given for two variables:

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the sample correlation coefficient?

y x

5 2

8 12

18 3

20 6

22 11

30 19

10 18

7 9

What is the sample correlation coefficient?