Question 1

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 fraction or proportion of the total data set that falls in that class. It is calculated by dividing the frequency of the class by the sample size, which is option D. Option A is incorrect because it involves dividing the midpoint of the class, which is not relevant to calculating relative frequency. Option B is incorrect because it involves dividing the frequency by the midpoint, which is not a meaningful calculation. Option C is incorrect because it involves dividing the sample size by the frequency of the class, which is not the correct formula for relative frequency.

Question 2

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

By definition, the sum of the deviations from the mean is always equal to zero.

Question 3

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 specifically designed to measure the linear association between two variables, so it is the best choice among the given options. The variance, coefficient of variation, and standard deviation are all measures of variability or dispersion, and do not specifically address the relationship between two variables.

Question 4

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

Accepted Answer

Covariance measures the direction of the linear relationship between two variables. A positive value of covariance indicates that there is a positive relation between the independent and dependent variables, which means that as the values of the independent variable increase, the values of the dependent variable also increase. A and B are incorrect because variance measures the spread of a single variable, not the relationship between two variables. C is incorrect because the standard deviation is a measure of variability and is not directly related to covariance.

Question 5

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, also known as Pearson's correlation coefficient, measures the strength and direction of a linear relationship between two variables. It can range from -1 to +1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and +1 indicates a perfect positive correlation. Therefore, option B is the best choice as it correctly states the range of the coefficient of correlation.

Question 6

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 the given alternatives is correct. The mode can be larger than the mean or smaller than the median. It is simply the value that occurs most frequently in the data set.

Question 7

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 8

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 9

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 is the average of the squared differences from the mean, while the standard deviation is the square root of the variance. Therefore, the variance can be larger or smaller than the numerical value of the standard deviation depending on the data. Option A is incorrect because the square of a real number is always non-negative, so the variance cannot be less than or equal to zero, which the standard deviation can be zero. Option B is incorrect because the standard deviation and variance are always non-negative. Option C is incorrect because the variance is always non-negative and cannot be negative just because the mean is negative.

Question 10

The symbol $\sigma$ is used to represent
A)the variance of the population
B)the standard deviation of the sample
C)the standard deviation of the population
D)the variance of the sample

Accepted Answer

The symbol used here is the Greek letter sigma (σ) which represents the standard deviation. The subscript 1 following the sigma indicates that it is the population standard deviation. Therefore, option C, standard deviation of the population, is the correct choice.

Question 11

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 12

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 the Pearson correlation coefficient, is a numerical value between -1 and 1 that measures the strength and direction of the linear relationship between two variables. A value of 1 represents a perfect positive linear correlation, a value of 0 represents no linear correlation, and a value of -1 represents a perfect negative linear correlation. Therefore, the coefficient of correlation cannot be larger than 1 or negative. Choice A is incorrect because while the coefficient of determination (r^2) is related to the coefficient of correlation, they are not the same thing. Choice B is also incorrect for the reason mentioned above.

Question 13

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

The coefficient of variation is defined as the standard deviation divided by the mean, expressed as a percentage. Given a coefficient of variation of 40% and a mean of 70, we can find the standard deviation as follows: $0.40 = \frac{\sigma}{70}$, solving for $\sigma$ gives $\sigma = 28$. The variance is the square of the standard deviation, so $28^2 = 784$.

Question 14

The symbol $\sigma$² is used to represent A)the variance of the population B)the standard deviation of the sample C)the standard deviation of the population D)the variance of the sample

Accepted Answer

The symbol $\sigma^2$ represents the variance of the population in statistics.

Question 15

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

Coefficient of variation (CV) is the ratio of the standard deviation to the mean, expressed as a percentage. 
CV = (Standard deviation / Mean) x 100%
0.64 = (8 / Mean) x 100%
Therefore, Mean = 8 / 0.64 = 12.5

Question 16

The measure of dispersion which is not measured in the same units as the original data is the
A)median
B)standard deviation
C)coefficient of determination
D)variance

Accepted Answer

The answer of The measure of dispersion which is not...

Question 17

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 is the average of the squares of the deviations from the mean. It is possible for all the numbers to be negative and still have a non-negative variance. Therefore, the variance must be at least zero.

Question 18

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

Accepted Answer

The numerical measure of linear association between two variables is the covariance. Variance and standard deviation are measures of variability, while coefficient of variation is a measure of relative variability. Therefore, the best choice is B.

Question 19

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 20

The variance of the sample
A)can never be negative
B)can be negative
C)cannot be zero
D)cannot be less than one

Accepted Answer

The variance is a measure of how spread out the data is from the mean, so it cannot be negative because it represents squared differences from the mean. It is always a non-negative number because the squared differences cannot be negative.

Quiz 3: Descriptive Statistics: Numerical Measures

The relative frequency of a class is computed by

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

A numerical measure of linear association between two variables is the

Positive values of covariance indicate

The coefficient of correlation ranges between

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

Which of the following is not a measure of dispersion?

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

The numerical value of the variance

The symbol $\sigma$ is used to represent

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?

The coefficient of correlation

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

The symbol $\sigma$ ² is used to represent

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

The measure of dispersion which is not measured in the same units as the original data is the

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 numerical measure of linear association between two variables is the

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

The variance of the sample

Quiz 3: Descriptive Statistics: Numerical Measures

The relative frequency of a class is computed by

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

A numerical measure of linear association between two variables is the

Positive values of covariance indicate

The coefficient of correlation ranges between

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

Which of the following is not a measure of dispersion?

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

The numerical value of the variance

The symbol σ\sigmaσ is used to represent

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?

The coefficient of correlation

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

The symbol σ\sigmaσ 2 is used to represent

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

The measure of dispersion which is not measured in the same units as the original data is the

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 numerical measure of linear association between two variables is the

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

The variance of the sample

The symbol $\sigma$ is used to represent

The symbol $\sigma$ ² is used to represent