Question 1

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, we need to first find the mean of the data set:

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

Next, we need to find the absolute deviation of each data point from the mean:

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

To find the mean absolute deviation, we need to find the average of these absolute deviations:

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

Therefore, the mean absolute deviation is 2.4, which is answer choice D.

Question 2

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 3

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%.

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 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 5

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 approximately 68% of the values in a bell-shaped set of data will fall within 1 standard deviation of the mean.

Question 6

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 7

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 smallest and the largest values, and the lower and upper quartiles.

Question 8

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 9

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 10

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 of the salaries, we first need to find the mean:

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

Then, we can calculate the variance using the formula:

Variance = ((33-39.25)^2 + (36-39.25)^2 + (41-39.25)^2 + (47-39.25)^2) / 4

Variance = 224.5 / 4

Variance = 56.125

Therefore, the variance of their salaries is approximately 37.58 (since we rounded to two decimal places).

Therefore, the best choice is C.

Question 11

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 12

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 13

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

Mode is the value that occurs most frequently in a data set. In this case, the value 92 occurs twice which is more than any other value, so the mode is 92.

Question 14

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

Accepted Answer

An outlier is determined using the interquartile range (IQR), which is calculated as the difference between the upper quartile (Q3) and the lower quartile (Q1). Any data point that falls more than 1.5 times the IQR above the upper quartile or below the lower quartile is considered an outlier.

Question 15

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

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

Question 16

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 median is the middle number when the numbers are arranged in order. Arranging the grades: 76, 79, 82, 86, 92, 92, 95. The middle number (4th in this case) is 86.

Question 17

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 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 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 time is the value that appears most frequently in the set of data. In this case, the time that appears most frequently is 41, which appears twice, while all other times appear only once. Therefore, the mode time required for this trip is 41.

Question 20

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 z score is used to standardize values and represents the number of standard deviations that a value is above or below the mean.

Quiz 3: Descriptive Statistics

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 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

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

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?

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

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

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 median time (in minutes) required for this trip was _______.

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?

An outlier of a data set is determined from 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 statistics student made the following grades on 7 tests: 76,82,92,95,79,86,and 92.What is the median grade?

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 _______.

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

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 _______.

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