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# Business Statistics Chapter 3

Chapter 3
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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
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...?
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
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
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
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
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
Positive
When the data are skewed to the right, the measure of skewness will be

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

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

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
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
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
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
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
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
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
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
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
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
Mode
Which of the following is not a measure of dispersion?

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
6
A researcher has collected the following sample data:
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...?
7
A researcher has collected the following sample data:
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...?
16.5
A researcher has collected the following 5 data points:
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...?
81.24%
A researcher has collected the following 5 data points:
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...?
6
A researcher has collected the following 5 data points:
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...?
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...?
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...?
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
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...?
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?
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?
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?