Question 1

A box and whisker plot is determined from the mean,the smallest and the largest values,and the lower and upper quartile.

Accepted Answer

A box and whisker plot is determined from the median, the lower and upper quartile, and the smallest and largest values, but not necessarily the mean.

Question 2

According to Chebyshev's Theorem how many values in a data set will be within 3 standard deviations of the mean?
A) At least 75%
B) At least 68%
C) At least 95%
D) At least 89%
E) At least 99%

Accepted Answer

Chebyshev's Theorem states that for any data set, regardless of distribution, at least (1 - 1/k^2) of the data values will fall within k standard deviations of the mean. For k=3, this is (1 - 1/3^2) = 1 - 1/9 = 8/9, which is approximately 89%.

Question 3

A sample was taken of the salaries of four employees from a large company.The following are their salaries (in thousands of dollars)for this year: 33,36,41,and 47.The variance of their salaries is approximately
A) 28.19
B) 75.59
C) 37.58
D) 6.13
E) 5.31

Accepted Answer

To find the variance, we need to first find the mean (average) of their salaries:

Mean = (33 + 36 + 41 + 47) / 4 = 39.25

Next, we need to find the difference between each salary and the mean, square each difference, and then find the average of those squared differences:

(33 - 39.25)^2 = 38.0625 
(36 - 39.25)^2 = 10.5625 
(41 - 39.25)^2 = 3.0625 
(47 - 39.25)^2 = 60.0625

Average of squared differences = (38.0625 + 10.5625 + 3.0625 + 60.0625) / 4 = 27.6875

Therefore, the variance is approximately 27.6875 thousand dollars squared.

To get the answer choices into the same units, we need to take the square root of the variance:

sqrt(27.6875) = 5.2638

Rounding to two decimal places, the answer is approximately 37.58 thousand dollars (C).

Question 4

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 34,39,41,35,and 41. The mean time (in minutes)required for this trip was _______.
A) 35
B) 41
C) 37.5
D) 38
E) 35.5

Accepted Answer

The answer of A commuter travels many miles to work...

Question 5

The number of standard deviations that a value (x)is above or below the mean is the _________________.
A) absolute deviation
B) coefficient of variation
C) interquartile range
D) z score
E) correlation coefficient

Accepted Answer

The definition provided is exactly the definition of a z score. It is a standardized value that represents how many standard deviations a data point is from the mean. Therefore, the correct choice is D - z score.

Question 6

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the median grade?
A)86
B) 76
C) 82
D) 94
E) 95

Accepted Answer

The answer of A statistics student made the following grades...

Question 7

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 38,33,36,47,and 41. What is the variance for this sample data?
A) 28.5
B) 11
C) 22.8
D) 5.34
E) 4.77

Accepted Answer

The answer of A commuter travels many miles to work...

Question 8

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the mode?
A) 79
B) 82
C) 86
D) 92
E) 76

Accepted Answer

The mode is the score that appears most frequently in the data set. In this case, 92 appears twice, which is more than any other score. Therefore, the mode is 92.

Question 9

The empirical rule says that approximately what percentage of the values would be within 2 standard deviations of the mean in a bell shaped set of data?
A) 95%
B) 68%
C) 50%
D) 97.7%
E) 100%

Accepted Answer

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 95% of the data falls within 2 standard deviations of the mean.

Question 10

The empirical rule says that approximately what percentage of the values would be within 1 standard deviation of the mean in a bell shaped set of data?
A) 95%
B) 68%
C) 50%
D) 97.7%
E) 100%

Accepted Answer

The empirical rule states that for a normally distributed dataset, approximately 68% of the values will fall within one standard deviation of the mean.

Question 11

A sample was taken of the salaries of four employees from a large company.The following are their salaries (in thousands of dollars)for this year: 33,36,41,and 47.The median of their salaries is approximately
A) 38.5
B) 34.5
C) 34
D) 44.5
E) 38

Accepted Answer

The median of a set of numbers is the middle value when the numbers are arranged in ascending order. For the given salaries of 33, 36, 41, and 47, when arranged in order, the middle values are 36 and 41. The median is the average of these two numbers: (36 + 41) / 2 = 77 / 2 = 38.5.

Question 12

The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours.We can conclude that at least 75% of this brand of bulbs will last between _______.
A) 1100 and 1300 hours
B) 1150 and 1250 hours
C) 1050 and 1350 hours
D) 1000 and 1400 hours
E) 950 and 1450 hours

Accepted Answer

The answer of The mean life of a particular brand...

Question 13

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 34,39,41,35,and 41. The mode time required for this trip was _______.
A) 39
B) 41
C) 37.5
D) 38
E) 35

Accepted Answer

The mode is the value that appears most frequently in the data set. In this case, the time of 41 minutes appears twice, which is more than any other value. Therefore, the mode time required for this trip is 41 minutes.

Question 14

An outlier of a data set is determined from the lower and upper quartile

Accepted Answer

Outliers in a data set are typically determined by calculating the interquartile range (IQR), which is the difference between the upper quartile (Q3) and the lower quartile (Q1). Outliers are then identified as those data points that fall below Q1 - 1.5*IQR or above Q3 + 1.5*IQR.

Question 15

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 38,33,36,47,and 41. What is the standard deviation for this sample data?
A) 28.5
B) 11
C) 22.8
D) 5.34
E) 4.77

Accepted Answer

The answer of A commuter travels many miles to work...

Question 16

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 44,39,41,35,and 41. What is the mean absolute deviation for this sample data?
A) 0
B) 12
C) 3
D) 2.4
E) 1.2

Accepted Answer

To find the mean absolute deviation (MAD), we first need to calculate the mean of the sample data:

Mean = (44+39+41+35+41)/5
Mean = 40

Next, we find the absolute deviation for each observation, which is the absolute value of the difference between each observation and the mean:

|44-40| = 4
|39-40| = 1
|41-40| = 1
|35-40| = 5
|41-40| = 1

Then, we find the average of these absolute deviations:

(4+1+1+5+1)/5 = 12/5

Therefore, the mean absolute deviation is 2.4, which is option D.

Question 17

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes)required to make this trip was 34,39,41,35,and 41. The median time (in minutes)required for this trip was _______.
A) 39
B) 41
C) 37.5
D) 38
E) 35.5

Accepted Answer

The median is the middle value when the data is arranged in order. Arranging the times in order gives 34, 35, 39, 41, 41. The middle value (median) is 39.

Question 18

If the median of a distribution is greater than mean,then the distribution is skewed to the left.

Accepted Answer

When the median is greater than the mean, it indicates that the distribution is skewed to the left (negatively skewed), meaning there are a few low values pulling the mean down more than the median.

Question 19

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the mean grade?
A) 78
B) 80
C) 86
D) 84
E) 88

Accepted Answer

The answer of A statistics student made the following grades...

Question 20

According to Chebyshev's Theorem,approximately how many values in a large data set will be within 2 standard deviations of the mean?
A) At least 75%
B) At least 68%
C) At least 95%
D) At least 89%
E) At least 99%

Accepted Answer

Chebyshev's Theorem states that for any dataset, regardless of the distribution, at least $1 - \frac{1}{k^2}$ of the data values will be within $k$ standard deviations of the mean. For $k = 2$, this gives $1 - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4}$ or 75%.

Quiz 3: Descriptive Statistics

A box and whisker plot is determined from the mean,the smallest and the largest values,and the lower and upper quartile.

According to Chebyshev's Theorem how many values in a data set will be within 3 standard deviations of the mean?

A sample was taken of the salaries of four employees from a large company.The following are their salaries (in thousands of dollars) for this year: 33,36,41,and 47.The variance of their salaries is approximately

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 34,39,41,35,and 41. The mean time (in minutes) required for this trip was _______.

The number of standard deviations that a value (x) is above or below the mean is the _________________.

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the median grade?

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 38,33,36,47,and 41. What is the variance for this sample data?

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the mode?

The empirical rule says that approximately what percentage of the values would be within 2 standard deviations of the mean in a bell shaped set of data?

The empirical rule says that approximately what percentage of the values would be within 1 standard deviation of the mean in a bell shaped set of data?

A sample was taken of the salaries of four employees from a large company.The following are their salaries (in thousands of dollars) for this year: 33,36,41,and 47.The median of their salaries is approximately

The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 50 hours.We can conclude that at least 75% of this brand of bulbs will last between _______.

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 34,39,41,35,and 41. The mode time required for this trip was _______.

An outlier of a data set is determined from the lower and upper quartile

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 38,33,36,47,and 41. What is the standard deviation for this sample data?

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 44,39,41,35,and 41. What is the mean absolute deviation for this sample data?

A commuter travels many miles to work each morning. She has timed this trip 5 times during the last month. The time (in minutes) required to make this trip was 34,39,41,35,and 41. The median time (in minutes) required for this trip was _______.

If the median of a distribution is greater than mean,then the distribution is skewed to the left.

A statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92. What is the mean grade?

According to Chebyshev's Theorem,approximately how many values in a large data set will be within 2 standard deviations of the mean?