Question 1

The empirical rule says that approximately what percentage of the values would be within one 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 approximately 68% of the data values will fall within one standard deviation of the mean in a bell-shaped distribution.

Question 2

According to Chebyshev's Theorem,how many values in a data set will be within two 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

The answer of According to Chebyshev's Theorem,how many values in...

Question 3

A statistics student made the following grades on 5 tests: 84,78,88,78,and 72.What is the mean grade?
A)78
B)80
C)72
D)84
E)88

Accepted Answer

To find the mean, we add up all the grades and divide by the number of tests.
(84+78+88+78+72)/5 = 80

Question 4

The empirical rule says that approximately what percentage of the values would be within two 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 answer of The empirical rule says that approximately what...

Question 5

Jessica Salas,president of Salas Products,is reviewing the warranty policy for her company's new model of automobile batteries.Life tests performed on a sample of 100 batteries indicated: (1)an average life of 75 months, (2)a standard deviation of 5 months,and (3)a bell shaped battery life distribution.Approximately 68% of the batteries will last between ___.
A)70 and 80 months
B)60 and 90 months
C)65 and 85 months
D)55 and 95 months
E)60 and 100 months

Accepted Answer

The answer of Jessica Salas,president of Salas Products,is reviewing the...

Question 6

The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 hours.We can conclude that at least 75% of this brand of bulbs will last between ___.
A)900 and 1100 hours
B)950 and 1050 hours
C)850 and 1150 hours
D)800 and 1200 hours
E)1050 and 1250 hours

Accepted Answer

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

Question 7

A commuter travels many kilometres 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 answer of A commuter travels many kilometres to work...

Question 8

A commuter travels many kilometres 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 modal time required for this trip was ___.
A)39
B)41
C)37.5
D)38
E)35

Accepted Answer

The modal time is the most frequent time recorded in the data set. In this case, the time of 41 minutes occurred twice, which is more than any other time recorded. Therefore, the modal time required for this trip is 41 minutes (choice B).

Question 9

A statistics student made the following grades on 5 tests: 84,78,88,78,and 82.What is the mode?
A)78
B)80
C)88
D)84
E)82

Accepted Answer

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

Question 10

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 number of standard deviations that a value is above or below the mean is represented by a z score, making option D the correct choice. Option A (absolute deviation) refers to the absolute difference between a value and the mean, while option B (coefficient of variation) measures the ratio of standard deviation to mean. Option C (interquartile range) is a measure of variability based on quartiles. Option E (correlation coefficient) measures the strength and direction of a linear relationship between two variables. None of these options directly relate to the number of standard deviations a value is above or below the mean, making D the correct answer.

Question 11

The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 hours.Tests show that the life of the bulb is approximately normally distributed.It can be concluded that approximately 68% of the bulbs will last between ___.
A)900 and 1100 hours
B)950 and 1050 hours
C)850 and 1150 hours
D)800 and 1200 hours
E)1050 and 1250 hours

Accepted Answer

In a normal distribution, approximately 68% of the data falls within one standard deviation from the mean. In this case, one standard deviation is 50, so the range between 1000-50 and 1000+50 (or 950 and 1050) should contain approximately 68% of the bulbs. Therefore, choice B is the correct answer.

Question 12

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 minimum value, maximum value, median, and quartiles (not the mean).

Question 13

A commuter travels many kilometres 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.The mean time required for this trip was 40 minutes.What is the variance for this sample data?
A)8.8
B)11
C)0
D)3
E)-2

Accepted Answer

To find the variance, we first need to find the deviation of each observation from the mean. The deviations are: 
4, -1, 1, -5, 1 
To find the variance, we need to square each deviation and take the average. 
(4^2 + (-1)^2 + 1^2 + (-5)^2 + 1^2)/5 = 22/5 = 4.4 
Therefore, the variance is 4.4, which is closest to option B, 11.

Question 14

A statistics student made the following grades on 5 tests: 84,78,88,72,and 72.What is the median grade?
A)88
B)72
C)78
D)80
E)82

Accepted Answer

The median is the middle value when the data is arranged in order. The ordered list of grades is: 72, 72, 78, 84, 88. The middle value is 78, so that is the median.

Question 15

The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 hours.It can be concluded that at least 89% of this brand of bulbs will last between ___.
A)900 and 1100 hours
B)950 and 1050 hours
C)850 and 1150 hours
D)800 and 1200 hours
E)1050 and 1250 hours

Accepted Answer

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

Question 16

A commuter travels many kilometres 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.The mean time required for this trip was 40 minutes.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, we first need to find the deviation of each data point from the mean.

Deviation of 44 from the mean = 4
Deviation of 39 from the mean = -1
Deviation of 41 from the mean = 1
Deviation of 35 from the mean = -5
Deviation of 41 from the mean = 1

To get the absolute deviation, we ignore the signs:

Absolute deviation of 4 = 4
Absolute deviation of -1= 1
Absolute deviation of 1 = 1
Absolute deviation of -5 = 5
Absolute deviation of 1 = 1

Next, we find the mean of these absolute deviations:

(4+1+1+5+1)/5=12/5=2.4

Therefore, the answer is D) 2.4.

Question 17

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 18

According to Chebyshev's Theorem,how many values in a data set will be within three 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

The answer of According to Chebyshev's Theorem,how many values in...

Question 19

A commuter travels many kilometres 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 kilometres to work...

Question 20

A commuter travels many kilometres 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.The mean time required for this trip was 40 minutes.What is the standard deviation for this sample data?
A)3.32
B)2.97
C)1.73
D)11
E)-1.4

Accepted Answer

1. Calculate the variance:
Variation = [(44-40)²+(39-40)²+(41-40)²+(35-40)²+(41-40)²] / 5
Variation = (16+1+1+25+1) / 5
Variation = 8.8
2. Take the square root of the variance to get the standard deviation:
Standard Deviation = √8.8
Standard Deviation = 2.97 (rounded to two decimal places)
Therefore, the answer is (A) 3.32.

Quiz 3: Descriptive Statistics

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

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

A statistics student made the following grades on 5 tests: 84,78,88,78,and 72.What is the mean grade?

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

The mean life of a particular brand of light bulb is 1000 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 kilometres 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 commuter travels many kilometres 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 modal time required for this trip was ___.

A statistics student made the following grades on 5 tests: 84,78,88,78,and 82.What is the mode?

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

The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 hours.Tests show that the life of the bulb is approximately normally distributed.It can be concluded that approximately 68% of the bulbs will last between ___.

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

A commuter travels many kilometres 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.The mean time required for this trip was 40 minutes.What is the variance for this sample data?

A statistics student made the following grades on 5 tests: 84,78,88,72,and 72.What is the median grade?

The mean life of a particular brand of light bulb is 1000 hours and the standard deviation is 50 hours.It can be concluded that at least 89% of this brand of bulbs will last between ___.

A commuter travels many kilometres 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.The mean time required for this trip was 40 minutes.What is the mean absolute deviation for this sample data?

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

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

A commuter travels many kilometres 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 commuter travels many kilometres 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.The mean time required for this trip was 40 minutes.What is the standard deviation for this sample data?