Deck 3: Statistical Description of Data

Question 1

Measures of dispersion describe typical values in the data.

Answer 1

False

Question 2

A standardized value that is either a large positive number or a large negative number is a relatively usual occurrence.

Answer 2

False

Question 3

Measures of central tendency and dispersion determined from frequency distributions are only approximations of the actual values.

Answer 3

True

Question 4

The mode is defined as the value that has just as many values above it as it has below it.

Question 5

The weights for a weighted mean calculation must sum up to 1.0.

Question 6

The mean of a set of values describes the 50th percentile.

Question 7

Which of the following is not a measure of central tendency?

A) Mean absolute deviation
B) Arithmetic mean
C) Weighted mean
D) Median
E) Mode

Question 8

Characteristics of the population are referred to as parameters,while characteristics of the sample are referred to as statistics.

Question 9

Percentiles divide the values into 100 parts of equal size,each comprising 1% of the observations.

Question 10

When a distribution has more values to the left and tails to the right,we say it is skewed negatively.

Question 11

Which of the following is not a measure of dispersion?

A) Mean absolute deviation
B) Quantiles
C) Weighted mean
D) Range
E) Standard deviation.

Question 12

The Empirical Rule states that approximately 68% of the observations in any distribution will fall within one standard deviation of the mean.

Question 13

Standardized values have no units,even though the original data,the standard deviation,and the mean may each represent units such as dollars,hours,or pounds.

Question 14

The box-and-whisker plot is a graphical device that simultaneously displays measures of central tendency and dispersion.

Question 15

The range is a measure of dispersion that includes all the values in the data set in the calculation.

Question 16

When a distribution has more values to the right and tails to the left,we say it is skewed positively.

Question 17

The measure of central tendency that is least affected by extreme values is the:

A) the weighted mean.
B) the mean.
C) the variance.
D) the standard deviation.
E) the median.

Question 18

The midrange is the average of the two middle data values.

Question 19

The measure of central tendency that is most affected by extreme values is the:

A) range.
B) mean.
C) median.
D) mode.
E) coefficient of variation.

Question 20

Which of the following statements is true regarding the normal distribution?

A) The mean is greater than the median and the median is greater than the mode.
B) The mean is less than the median and the median is less than the mode.
C) There is no difference in the values of the mean,median,and mode.
D) The mean is greater than the mode,which in turn is greater than the median.
E) The mean is less than the mode,which in turn is less than the median.

Question 21

A study was conducted of the 12-month earnings per share for two categories of airline companies. $$\begin{array} { | c | c | } \hline \text { Large Airlines } & \text { Small Airlines } \\\hline \$ 4.36 & \$ 1.60 \\6.19 & - 1.98 \\- 0.42 & 1.03 \\3.73 & - 0.21 \\0.26 & - 1.15 \\6.27 & 4.19 \\& 0.59 \\& 1.52 \\& 1.97 \\& 4.57 \\& 0.05 \\\hline\end{array}$$ Based on the above data,which of the following statements is correct?

A) The large airlines have a coefficient of variation of 2.44 while the small airlines have a coefficient of variation of 3.64.
B) Because the large airlines have mean earnings per share of 3.40 and the small airlines have mean earnings per share of 1.11,the large airlines have the largest coefficient of variation.
C) Because the large airlines have mean earnings per share of 3.54 and the small airlines have mean earnings per share of 1.71,the large airlines have the largest coefficient of variation.
D) The large airlines have a coefficient of variation of 0.85 and the small airlines have a coefficient of variation of 2.72.
E) The large airlines have a coefficient of variation of 0.81 and the small airlines have a coefficient of variation of 1.17.

Question 22

Which of the following is not a measure of variability?

A) The range
B) The variance
C) The standard deviation
D) The median
E) The interquartile range

Question 23

The difference between the largest and smallest values in a data set is called the:

A) standard deviation.
B) variance.
C) coefficient of variation.
D) range.
E) mean.

Question 24

Which of the following is not a correct statement?

A) The coefficient of variation allows us to compare two sets of data based on different measurement units.
B) Chebyshev's theorem applies only to normal distributions.
C) Standardized values have no units of measure.
D) For distributions that are bell-shaped and symmetric,about 68% of the observations will fall within one standard deviation of the mean.
E) The vertical line within the box in the box-and-whisker plot represents the median.

Question 25

The average score for a class of 25 students was 75.If the 15 female students in the class averaged 70,then the male students in the class averaged:

A) 85.0
B) 82.5
C) 77.5
D) 75.0
E) 70.0

Question 26

Which of the measures of central tendency would best represent the data below? $$\begin{array} { | l | c | } \hline \text { Project Management Software } & \text { Price (\$) } \\\hline \text { APECS } & 55,000 \\\text { The Chief Software: Project } & 3,900 \\\text { Management } & 249 \\\text { CPM/PERT } & 50 \\\text { Demi Plan } & 115 \\\text { Expert } & 395 \\\text { Harvard Project Manager } & 249 \\\text { Intepert } & 695 \\\text { LISA7/7 } & 395 \\\text { Micro Trak } & 595 \\\text { Milestone } & 250 \\\text { Pathfinder } & 299 \\\text { PC-PATH } & 995 \\\text { Plan/Trax } & 795 \\\text { Pro-Ject 6 } & 199 \\\text { Task } & 329 \\\hline\end{array}$$

A) Range
B) Mean
C) Median
D) Mode
E) Standard deviation

Question 27

Which of the following statements is correct?

A) The range is found by taking the difference between the high and low values and dividing by 2.
B) The interquartile range is found by taking the difference between the 1st and 3rd quartiles and dividing that value by 2.
C) The standard deviation is expressed in terms of the original units of measurement but the variance is not.
D) The values of the standard deviation may be either positive or negative,while the value of the variance will always be positive.
E) None of these statements is true.

Question 28

In a negatively skewed distribution,the:

A) mean is greater than the median and the median is greater than the mode.
B) mean is greater than the median and the median is smaller than the mode.
C) mean is smaller than the median and the median is greater than the mode.
D) mean is smaller than the median and the median is smaller than the mode.
E) mean is equal to the median and the median is equal to the mode.

Question 29

Which of the following statements is correct?

A) The mean is a measure of the deviation in a data set.
B) The standard deviation is a measure of dispersion.
C) The range is a measure of central tendency.
D) The median is a measure of dispersion.
E) The variance is a measure of central tendency.

Question 30

Expressed in percentiles,the interquartile range is the difference between the:

A) 15th and 65th percentiles
B) 20th and 70th percentiles
C) 25th and 75th percentiles
D) 30th and 80th percentiles
E) 35th and 85th percentiles

Question 31

Chebyshev's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is:

A) 90%.
B) at least 90%.
C) 96%.
D) at least 96%.
E) 25%.

Question 32

Which of the following is the simplest measure of dispersion?

A) Range
B) Mean absolute deviation
C) Standard deviation
D) Coefficient of variation
E) Variance

Question 33

Deciles:

A) are an array of values in 10 parts of equal size.
B) indicate the median with the fifth decile.
C) divide the values into four parts of equal size.
D) indicate the median with the second decile.
E) both A and B are correct.

Question 34

Which of the following statements are true for the following data values: 9,7,8,6,9,10,and 14?

A) The mean,median and mode are all equal
B) Only the mean and median are equal
C) Only the mean and mode are equal
D) Only the median and mode are equal

Question 35

When a distribution is bell-shaped with the left half identical to the right half,it is:

A) skewed positively
B) symmetrical
C) equilateral
D) skewed negatively
E) not applicable for Chebyshev's theorem

Question 36

In a positively skewed distribution,the:

A) mean is greater than the median and the median is greater than the mode.
B) mean is greater than the median and the median is smaller than the mode.
C) mean is smaller than the median and the median is greater than the mode.
D) mean is smaller than the median and the median is smaller than the mode.
E) mean is equal to the median and the median is equal to the mode.

Question 37

The Empirical Rule states that the percentage of observations in a data set (providing that the data set has a bell-shaped and symmetric distribution)that fall within one standard deviation of their mean is approximately:

A) 68%
B) 75%
C) 95%
D) 99%

Question 38

Which of the following statements is correct?

A) The mode gives equal consideration to even very extreme values in the data.
B) There will be just one value for the mean,median ,and mode in the data set.
C) The median can be strongly influenced by just one or two very low or high values.
D) The mean is able to make the most complete use of the data when compared to the median and mode.
E) None of the above are correct.

Question 39

The value in the data set that occurs with the greatest frequency is known as the:

A) mode.
B) median.
C) mean.
D) weighted mean.
E) variance.

Question 40

A sample of 15 observations has a standard deviation of 4.The sum of the squared deviations from the sample mean is:

A) 19
B) 56
C) 60
D) 224
E) 240

Question 41

Sample values of 13 monthly sales figures (in thousands of dollars)are: 6,5,6,6,7,8,9,10,10,10,9,9,and 6.
What is the mean sales figure?
____________________ thousand

Question 42

If the coefficient of correlation ,then the best-fit linear equation will include:

A) 75% of the data points.
B) 85% of the data points.
C) 95% of the data points.
D) all of the data points.

Question 43

The average profit per unit for Product A is $5.32,Product B is $7.98,and Product C is $9.69.If the percentages of each sold are 36,29,and 35 respectively,what is the weighted mean profit per unit?

Question 44

For a set of data,the mean is 50 and the standard deviation is 10.In the raw data,one of the observations is equal to 74.After the data are standardized,what will be the standardized value of this observation?

A) +7.4
B) -7.4
C) +2.4
D) -2.4

Question 45

The length of the box in the box-and-whisker plot portrays the:

A) mean
B) median
C) range
D) interquartile range

Question 46

If the coefficient of correlation r = 0,then:

A) the slope of the regression line is zero.
B) there is no linear relationship whatsoever between the dependent variable y and the independent variable x.
C) the coefficient of determination is zero.
D) All of these are correct.
E) None of these is correct.

Question 47

The numerical value of the coefficient of determination r ²

A) is the proportion of the variation in the dependent variable y that is explained by the best-fit linear equation.
B) is the proportion of the variation in the independent variable x that is explained by the best-fit linear equation.
C) indicates the direction of the relationship between the dependent variable y and the independent variable x.
D) Both A and B are correct.
E) A,B,and C are all correct.

Question 48

Which of the following statements is not correct?

A) Measures of central tendency determined from frequency distributions will only be approximations of the actual values.
B) Measures of dispersion determined from frequency distributions will only be approximations of the actual values.
C) In grouped data,each observation is given the value of its classification's mid-point.
D) When data are grouped,the value of each individual observation is lost.
E) All of the above statements are correct.

Question 49

When the standard deviation is expressed as a percentage of the mean,the result is the:

A) coefficient of correlation.
B) coefficient of determination.
C) coefficient of variation.
D) coefficient of dispersion.

Question 50

You are interested in beginning a small business enterprise and one aspect of your research is to look at the loan record for stockholders of small business corporations.A14-year record of net loans from stockholders of small business corporations (in billions of dollars)are as follows: 1.6,-0.2,1.0,1.4,-0.1,0.6,1.5,0.9,2.2,1.3,1.9,1.9,2.8,and 5.0.
Calculate the mode.
____________________ billion

Question 51

For each of the past 10 years,the U.S.unemployment rate has been recorded as follows: 6.7,5.5,5.7,5.2,4.5,3.8,3.8,3.6,3.5,and 4.9.Find the mean unemployment rate for this period.

Question 52

You are interested in beginning a small business enterprise and one aspect of your research is to look at the loan record for stockholders of small business corporations.A14-year record of net loans from stockholders of small business corporations (in billions of dollars)are as follows: 1.6,-0.2,1.0,1.4,-0.1,0.6,1.5,0.9,2.2,1.3,1.9,1.9,2.8,and 5.0.
Calculate the median.
____________________ billion

Question 53

A student scores 89,72,93,and 84 on four exams during the semester and 96 on the final exam.If the final is weighted double and the four others weighted equally,what would the student's final average be?

Question 54

The coefficient of correlation r is a number that indicates the:

A) direction of the relationship between the dependent variable y and the independent variable x.
B) strength of the relationship between the dependent variable y and the independent variable x.
C) proportion of the variation in the dependent variable y that is explained by the independent variable x.
D) Only A and B are correct.
E) A,B,and C are all correct.

Question 55

A perfect straight line sloping upward would produce a correlation coefficient equal to:

A) +1.
B) -1.
C) +2.
D) -2.

Question 56

You are interested in beginning a small business enterprise and one aspect of your research is to look at the loan record for stockholders of small business corporations.A14-year record of net loans from stockholders of small business corporations (in billions of dollars)are as follows: 1.6,-0.2,1.0,1.4,-0.1,0.6,1.5,0.9,2.2,1.3,1.9,1.9,2.8,and 5.0.
Calculate the mean.
____________________ billion

Question 57

A sample of 10 U.S.families spent the following amounts (in dollars)on groceries during a one-week period: 31.36,68.76,12.25,10.85,24.89,31.48,49.52,48.24,30.04,and 25.63.Find the median amount spent on groceries.

Question 58

A sample of interest rates on unpaid credit card balances yields the following data: 13.25,13.67,13.60,13.29,12.97,12.90,12.76,12.66,12.58,12.77,and 12.91.Find the median interest rate.

Question 59

Heidi has been keeping track of what she spends to eat out.The last week's expenditures (in dollars)for meals eaten out were 3.69,3.95,4.19,8.91,5.49,12.53,and 5.66.Calculate the mean amount she spent on meals last week.

Question 60

The difference between the mean of a data set and the individual values of that set is known as the:

A) variance
B) standard deviation
C) residual
D) mean absolute deviation
E) quartile

Question 61

NARRBEGIN: Sample data
Consider the following sample data: 6,10,4,3,7,9,21,and 14.
Consider the following sample data: 6,10,4,3,7,9,21,and 14.What is the range of this data sample?

Question 62

In a test of a lifelong brand of tires,a survey revealed that the mean life was 35,000 miles and the standard deviation was 7,083 miles.If the shape of the population distribution is not known,approximately what percentage of the tires last less than 20,834 miles?

Question 63

NARRBEGIN: Pizza
In preparation for a pizza party,the students at State University surveyed the price of medium-sized pizzas for local restaurants:
What is the mid-range?

Question 64

What is the coefficient of variation of the following sample data set: 12,9,5,23,11,8,16,and 6?

Question 65

Sample values of 13 monthly sales figures (in thousands of dollars)are: 6,5,6,6,7,8,9,10,10,10,9,9,and 6.
What is the median sales figure?
____________________ thousand

Question 66

NARRBEGIN: TV Markets
The top twenty TV markets in the United States are:
What is the median?
____________________

Question 67

NARRBEGIN: Sample data
Consider the following sample data: 6,10,4,3,7,9,21,and 14.
Consider the following sample data: 6,10,4,3,7,9,21,and 14.What is the mean absolute deviation?

Question 68

NARRBEGIN: Sample data
Consider the following sample data: 6,10,4,3,7,9,21,and 14.
Consider the following sample data: 6,10,4,3,7,9,21,and 14.What is the variance?

Question 69

Sample values of 13 monthly sales figures (in thousands of dollars)are: 6,5,6,6,7,8,9,10,10,10,9,9,and 6.
What is the mode?
____________________ thousand

Question 70

NARRBEGIN: TV Markets
The top twenty TV markets in the United States are:
What is the first quartile?
____________________

Question 71

Consider the following sample data: 4,14,6,9,21,3,7,and 10.
Calculate the mean.

Question 72

A sample of 13 monthly sales figures (in thousands of dollars)are: 10,6,5,10,9,7,10,9,6,8,9,6,and 6.
Calculate the mean absolute deviation.

Question 73

Consider the following sample data: 4,14,6,9,21,3,7,and 10.
Calculate the median.

Question 74

A sample of 13 monthly sales figures (in thousands of dollars)are: 10,6,5,10,9,7,10,9,6,8,9,6,and 6.
Calculate the sample standard deviation.

Question 75

Find the midrange for the following data: 14,99,53,67,16,55,and 11.

Question 76

NARRBEGIN: Sample data
Consider the following sample data: 6,10,4,3,7,9,21,and 14.
Consider the following sample data: 6,10,4,3,7,9,21,and 14.What is the standard deviation?

Question 77

A sample of 13 monthly sales figures (in thousands of dollars)are: 10,6,5,10,9,7,10,9,6,8,9,6,and 6.
What is the sample variance?

Question 78

A sample of 13 monthly sales figures (in thousands of dollars)are: 10,6,5,10,9,7,10,9,6,8,9,6,and 6.
What is the coefficient of variation?

Question 79

Find the range for the following data: 9,94,48,62,11,50,and 6.

Question 80

NARRBEGIN: Pizza
In preparation for a pizza party,the students at State University surveyed the price of medium-sized pizzas for local restaurants:
What is the range of these prices?