Question 1

Since the median is the middle value of a data set it
A)must always be smaller than the mode
B)must always be larger than the mode
C)must always be smaller than the mean
D)None of these alternatives is correct.

Accepted Answer

None of these alternatives is correct. The relationship between the median, mode, and mean depends on the shape of the data set's distribution. In some cases, the median may be larger than the mean, and in others, the mode may be larger than both the mean and the median.

Question 2

During a cold winter,the temperature stayed below zero for ten days (ranging from -20 to -5).The variance of the temperatures of the ten-day period
A)is negative since all the numbers are negative
B)must be at least zero
C)cannot be computed since all the numbers are negative
D)can be either negative or positive

Accepted Answer

The variance of a set of numbers cannot be negative, as it represents the average distance of the numbers from their mean. Therefore, the answer cannot be A or C. The variance can be zero if all the numbers are the same, but since the temperatures range from -20 to -5, this is not the case. Thus, the only valid option is B - the variance must be at least zero.

Question 3

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.

Accepted Answer

None of these alternatives is correct. The mode can be smaller, equal to, or larger than both the mean and the median.

Question 4

A numerical measure of linear association between two variables is the
A)variance
B)coefficient of variation
C)correlation coefficient
D)standard deviation

Accepted Answer

The correlation coefficient is a numerical measure of linear association between two variables. It ranges from -1 to 1, with positive values indicating a positive association and negative values indicating a negative association. A value of 0 indicates no linear association between the two variables. The other choices (variance, coefficient of variation, and standard deviation) are measures of variability or dispersion, not of association.

Question 5

Which of the following is not a measure of dispersion?
A)mode
B)standard deviation
C)range
D)interquartile range

Accepted Answer

Mode is a measure of central tendency, not dispersion.

Question 6

Given the following information:
Standard deviation = 8
Coefficient of variation = 64%
The mean would then be
A)12.5
B)8
C)0.64
D)1.25

Accepted Answer

The coefficient of variation is calculated as (Standard Deviation / Mean) * 100. Given a coefficient of variation of 64% and a standard deviation of 8, we can solve for the mean: (8 / Mean) * 100 = 64. Solving for the mean gives us 12.5.

Question 7

If the coefficient of variation is 40% and the mean is 70,then the variance is
A)28
B)2800
C)1.75
D)784

Accepted Answer

We know that the coefficient of variation formula is:

Coefficient of Variation = (Standard Deviation / Mean) x 100%

Given that coefficient of variation is 40% and mean is 70, we can write:

40% = (Standard Deviation / 70) x 100%

Solving for Standard Deviation, we get:

Standard Deviation = (40/100) x 70 = 28

We also know that variance is equal to the square of standard deviation, so:

Variance = Standard Deviation^2 = 28^2 = 784

Therefore, the correct answer is D (784).

Question 8

The standard deviation of a sample was reported to be 20.The report indicated that 
= 7200.What has been the sample size?
A)16
B)17
C)18
D)19

Accepted Answer

The answer of The standard deviation of a sample was...

Question 9

In a five number summary,which of the following is not used for data summarization?
A)the smallest value
B)the largest value
C)the mean
D)the 25th percentile

Accepted Answer

The five number summary includes the smallest value, the largest value, the median, and the 25th and 75th percentiles. The mean is not used in the five number summary, as it is a measure of central tendency that can be influenced by outliers.

Question 10

The numerical value of the variance
A)is always larger than the numerical value of the standard deviation
B)is always smaller than the numerical value of the standard deviation
C)is negative if the mean is negative
D)can be larger or smaller than the numerical value of the standard deviation

Accepted Answer

The variance can be either larger or smaller than the standard deviation, depending on the size of the standard deviation. The variance is equal to the square of the standard deviation, so when the standard deviation is small, the variance will be much smaller. However, when the standard deviation is large, the variance will be much larger. Therefore, it is not true that the variance is always larger or smaller than the standard deviation. The variance can also be negative if the data values are far below the mean, but this is not necessarily related to the sign of the mean.

Question 11

Exhibit 3-1
The following data show the number of hours worked by 200 statistics students.
 
-Refer to Exhibit 3-1.The class width for this distribution
A)is 9
B)is 10
C)is 11
D)varies from class to class

Accepted Answer

The difference between the smallest and largest data points is 58, so if we divide by the desired number of classes (which is not given in the exhibit), we could end up with a non-integer class width. However, if we choose 20 as the number of classes, we get a class width of 58/20=2.9, which rounded up to the nearest whole number is 3. Multiplying 3 by 3, we get a class width of 9, which is closest to one of the answer choices, B. Therefore, B is the best choice.

Question 12

From a population of size 500,a random sample of 50 items is selected.The mode of the sample
A)must be 500
B)must be equal to the mode of population,if the sample is truly random
C)must be equal to the mean of the population,if the sample is truly random
D)can be larger,smaller or equal to the mode of the population

Accepted Answer

The mode of the sample can be different from the mode of the population since the sample is a random selection. It is possible that a particular value appears more frequently in the sample than in the population, thus resulting in a different mode. Therefore, the mode of the sample can be larger, smaller, or equal to the mode of the population.

Question 13

The relative frequency of a class is computed by
A)dividing the midpoint of the class by the sample size
B)dividing the frequency of the class by the midpoint
C)dividing the sample size by the frequency of the class
D)dividing the frequency of the class by the sample size

Accepted Answer

The relative frequency of a class is the proportion of data points that fall into that particular class. It is computed by dividing the frequency of the class by the total number of data points in the sample. Therefore, the best choice is D, which divides the frequency of the class by the sample size.

Question 14

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

Accepted Answer

The coefficient of correlation (also known as Pearson's correlation coefficient) measures the strength and direction of the linear relationship between two variables, and it ranges from -1 to 1. A value of -1 indicates a perfect negative correlation, a value of 0 indicates no correlation, and a value of 1 indicates a perfect positive correlation. Therefore, the coefficient of correlation cannot be larger than 1 or smaller than -1.

Question 15

A group of students had dinner at a local restaurant.The total bill for the dinner was $414.70.Each student paid his/her equal share of the bill,which was $18.85.How many student's were at the dinner?
A)4
B)415
C)19
D)22

Accepted Answer

The answer of A group of students had dinner at...

Question 16

From a population of size 400,a random sample of 40 items is selected.The median of the sample
A)must be 200,since 400 divided by 2 is 200
B)must be 10,since 400 divided by 400 is 10
C)must be equal to the median of population,if the sample is truly random
D)None of these alternatives is correct.

Accepted Answer

The answer of From a population of size 400,a random...

Question 17

The coefficient of correlation ranges between
A)0 and 1
B)-1 and +1
C)minus infinity and plus infinity
D)1 and 100

Accepted Answer

The coefficient of correlation is a measure of the linear relationship between two variables, and it ranges between -1 and +1. A coefficient of -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and +1 indicates a perfect positive linear relationship. Therefore, choice B (-1 and +1) is the correct range for the coefficient of correlation.

Question 18

From a population of size 1,000,a random sample of 100 items is selected.The mean of the sample
A)must be 10 times smaller than the mean of the population
B)must be equal to the mean of the population,if the sample is truly random
C)must be 10 times larger than the mean of the population
D)can be larger,smaller or equal to the mean of the population

Accepted Answer

The mean of a sample can vary due to random sampling variability, meaning it can be larger, smaller, or equal to the population mean, depending on the specific items selected in the sample.

Question 19

The value of the sum of the deviations from the mean,i.e. , 
Must always be
A)less than the zero
B)negative
C)either positive or negative depending on whether the mean is negative or positive
D)zero

Accepted Answer

The value of the sum of the deviations from the mean is always zero. This is because the sum of the deviations above the mean is equal to the sum of the deviations below the mean. Therefore, they cancel each other out and the sum of the deviations is zero.

Question 20

The variance of a sample was reported to be 144.The report indicated that 
= 7200.What has been the sample size?
A)49
B)50
C)51
D)52

Accepted Answer

The answer of The variance of a sample was reported...

Quiz 3: Descriptive Statistics: Numerical Measures

Since the median is the middle value of a data set it

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

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

A numerical measure of linear association between two variables is the

Which of the following is not a measure of dispersion?

Given the following information: Standard deviation = 8 Coefficient of variation = 64% The mean would then be

If the coefficient of variation is 40% and the mean is 70,then the variance is

The standard deviation of a sample was reported to be 20.The report indicated that = 7200.What has been the sample size?

In a five number summary,which of the following is not used for data summarization?

The numerical value of the variance

Exhibit 3-1 The following data show the number of hours worked by 200 statistics students. -Refer to Exhibit 3-1.The class width for this distribution

From a population of size 500,a random sample of 50 items is selected.The mode of the sample

The relative frequency of a class is computed by

The coefficient of correlation

A group of students had dinner at a local restaurant.The total bill for the dinner was $414.70.Each student paid his/her equal share of the bill,which was $18.85.How many student's were at the dinner?

From a population of size 400,a random sample of 40 items is selected.The median of the sample

The coefficient of correlation ranges between

From a population of size 1,000,a random sample of 100 items is selected.The mean of the sample

The value of the sum of the deviations from the mean,i.e. , Must always be

The variance of a sample was reported to be 144.The report indicated that = 7200.What has been the sample size?