Deck 4: Descriptive Statistical Measures

Question 1

Compare and contrast methods of summarizing and describing data
Use the table below to answer the following question(s).
Below is a table showing the costs per order of items bought by a computer hardware store. $$\begin{array} { | l | l | l | } \hline \text { Supplier } & \text { Item Description } & \text { Cost per Order } \\\hline \text { Aloham Technologies } & \text { Monitors } & \$ 250 \\\hline \text { Aloham Technologies } & \text { Hard Disks } & \$ 220 \\\hline \text { Aloham Technologies } & \text { Power Supply } & \$ 88 \\\hline \text { Aloham Technologies } & \text { Graphics Card } & \$ 300 \\\hline \text { Aloham Technologies } & \text { Processor } & \$ 325 \\\hline \text { Aloham Technologies } & \text { Speakers } & \$ 88 \\\hline \text { MindRoot Hardwares } & \text { Flashdrive } & \$ 9 \\\hline \text { MindRoot Hardwares } & \text { Graphics Card } & \$ 299 \\\hline \text { MindRoot Hardwares } & \text { CD-ROM } & \$ 88 \\\hline \text { MindRoot Hardwares } & \text { Bluetooth Device } & \$ 80 \\\hline\end{array}$$

-Calculate the mode for the cost per order data.

A) $174.17
B) $325
C) $88
D) $206.5

Answer 1

$88

Question 2

Which of the following is a difference between a mean and a median?

A) A mean divides the data half above it and half below it; a median does not.
B) A median is not affected by outliers; a mean is affected by outliers.
C) A mean is an observation that occurs most frequently; a median is the average of all observations.
D) A median is not meaningful for ratio data; a mean is meaningful to ratio data.

Answer 2

B

Question 3

Which of the following is an example of a subset?

A) The number of individuals who have a Ford car
B) The number of IT employees out of all employees working in an office of Google
C) The number of members in the Democratic Party
D) The population of Canada

Answer 3

B

Question 4

Which of the following is true for a median?

A) A median is only meaningful for interval or ordinal data and not for ratio data.
B) Medians can be calculated no matter how the data is arranged.
C) Medians are affected by outliers.
D) For an even number of observations, the median is the mean of the two middle numbers.

Question 5

The difference between the first and third quartiles is referred to as the .

A) standard deviation
B) variance
C) interquartile range
D) midrange

Question 6

Which of the following is true for a mode?

A) Modes are the mid values of data arranged from least to greatest.
B) Modes are affected by outliers.
C) Modes cannot be used in data having repetitious values.
D) The highest bar in a histogram is its mode.

Question 7

Which of the following is an example of a measure of dispersion?

A) median
B) mode
C) variance
D) midrange

Question 8

According to statistical notations, what does Σ stand for?

A) to act as a summation operator
B) to represent sample statistics
C) to represent population measures
D) to represent the number of items in a population

Question 9

In statistical notation, the elements of a data set are typically labeled as .

A) summation operators
B) letters in capitals
C) Greek letters
D) subscripted variables

Question 10

The is the observation that occurs most frequently.

A) mode
B) mean
C) outlier
D) median

Question 11

The purpose of sampling is to .

A) enumerate all the values in the population
B) measure all items of interest for a particular interest or investigation
C) obtain sufficient information to draw a valid inference about a population
D) calculate all variables and observations within a population

Question 12

The measure of location that specifies the middle value when the data are arranged from least to greatest is the .

A) outlier
B) mean
C) median
D) mode

Question 13

One of the measures of location is calculated as 88. Which of the following measures of location corresponds to this value?

A) mean
B) mode
C) median
D) midrange

Question 14

Which of the following describes dispersion in statistics?

A) the degree of variation in the data
B) the central value in the data
C) the frequency of values in the data
D) the measure of outliers in the data

Question 15

Which of the following types of conditions is most likely to render a midrange value useless?

A) having repetitious values in the data set
B) having the data arranged from least to greatest in value
C) having a small sample size
D) having extreme values in a data

Question 16

Which of the following is true of midspread?

A) It is an example of a measure of location.
B) It is calculated by finding the difference between the highest and lowest values in the data set.
C) It is affected by extreme values.
D) It is calculated using only the middle 50% of the data.

Question 17

Compare and contrast methods of summarizing and describing data
Use the table below to answer the following question(s).
Below is a table showing the costs per order of items bought by a computer hardware store. $$\begin{array} { | l | l | l | } \hline \text { Supplier } & \text { Item Description } & \text { Cost per Order } \\\hline \text { Aloham Technologies } & \text { Monitors } & \$ 250 \\\hline \text { Aloham Technologies } & \text { Hard Disks } & \$ 220 \\\hline \text { Aloham Technologies } & \text { Power Supply } & \$ 88 \\\hline \text { Aloham Technologies } & \text { Graphics Card } & \$ 300 \\\hline \text { Aloham Technologies } & \text { Processor } & \$ 325 \\\hline \text { Aloham Technologies } & \text { Speakers } & \$ 88 \\\hline \text { MindRoot Hardwares } & \text { Flashdrive } & \$ 9 \\\hline \text { MindRoot Hardwares } & \text { Graphics Card } & \$ 299 \\\hline \text { MindRoot Hardwares } & \text { CD-ROM } & \$ 88 \\\hline \text { MindRoot Hardwares } & \text { Bluetooth Device } & \$ 80 \\\hline\end{array}$$

-Calculate the mean cost per order.

A) $220.54
B) $174.70
C) $159
D) $88

Question 18

Which of the following is a similarity between a midrange and a mean?

A) Both measures are calculated using all the values in a data set.
B) Both measures are affected by outliers.
C) Both measures divide the data into two equal halves.
D) Both measures can only be used for small sample sizes.

Question 19

Compare and contrast methods of summarizing and describing data
Use the table below to answer the following question(s).
Below is a table showing the costs per order of items bought by a computer hardware store. $$\begin{array} { | l | l | l | } \hline \text { Supplier } & \text { Item Description } & \text { Cost per Order } \\\hline \text { Aloham Technologies } & \text { Monitors } & \$ 250 \\\hline \text { Aloham Technologies } & \text { Hard Disks } & \$ 220 \\\hline \text { Aloham Technologies } & \text { Power Supply } & \$ 88 \\\hline \text { Aloham Technologies } & \text { Graphics Card } & \$ 300 \\\hline \text { Aloham Technologies } & \text { Processor } & \$ 325 \\\hline \text { Aloham Technologies } & \text { Speakers } & \$ 88 \\\hline \text { MindRoot Hardwares } & \text { Flashdrive } & \$ 9 \\\hline \text { MindRoot Hardwares } & \text { Graphics Card } & \$ 299 \\\hline \text { MindRoot Hardwares } & \text { CD-ROM } & \$ 88 \\\hline \text { MindRoot Hardwares } & \text { Bluetooth Device } & \$ 80 \\\hline\end{array}$$

-Calculate the median for the cost per order data.

A) $325
B) $154
C) $174.17
D) $88

Question 20

The is the average of the greatest and least values in the data set.

A) mean
B) median
C) midrange
D) mode

Question 21

In the equation Cp = (upper specification - lower specification)/total variation, what does Cp denote?

A) capacity variation index
B) capability pattern
C) process capability index
D) capability push

Question 22

Which of the following is true of the coefficient of skewness (CS)?

A) If the CS is positive, the distribution of values tails off to the left.
B) If the CS value is between 0.5 and 1, the skewness is considered to be moderate.
C) If the CS is closer to zero, the degree of skewness is considered to be high.
D) If the CS value is between -0.5 and -1, the skewness is considered negligible.

Question 23

states that for any set of data, the proportion of values that lie within k standard deviations (k > 1) of the mean is at least 1 - 1/k².

A) Prime number theorem
B) Bertrand's postulate
C) Oppermann's conjecture
D) Chebyshev's theorem

Question 24

The is a formal statistical measure for categorical data, such as defects or errors in quality control applications or consumer preferences in market research.

A) variance
B) proportion
C) mean
D) skewness

Question 25

Using Chebyshev's theorem for standard deviation, calculate the percentage of data that lie within five standard deviations of the mean.

A) 89%
B) 75%
C) 96%
D) 50%

Question 26

Which of the following describes a positively skewed histogram?

A) a histogram that tails off toward the right
B) a histogram that has no fluctuation in mass
C) a histogram where more mass tails off toward the left
D) a histogram where mass is only concentrated in the middle

Question 27

How is the return to risk described in financial statistics?

A) as the relative measure of the distance an observation is from the mean
B) as the reciprocal of coefficient of variation
C) as the square root of variance
D) as the ratio of excess returns to its standard deviation

Question 28

Which of the following describes variance?

A) It is the difference between the maximum value and the minimum value in the data set.
B) It is the difference between the first and third quartiles of a data set.
C) It is the average of the squared deviations of the observations from the mean.
D) It is the average of the greatest and least values in the data set.

Question 29

In finance, the is the ratio of a fund's excess returns (annualized total returns minus Treasury bill returns) to its standard deviation.

A) field ratio
B) Sortino ratio
C) Calmar ratio
D) Sharpe ratio

Question 30

is a measure of the linear association between two variables, X and Y.

A) Kurtosis
B) Proportion
C) Skewness
D) Covariance

Question 31

The measures the degree of asymmetry of observations around the mean.

A) coefficient of variation
B) return to risk factor
C) coefficient of skewness
D) coefficient of kurtosis

Question 32

Which of the following is true of variance?

A) The formula to calculate variance of a population is not the same as the formula to calculate variance of a sample.
B) Its value is inversely proportional to the degree to which the data is spread from the mean.
C) It only requires the middle 50% of data to be calculated.
D) It is the square root of standard deviation.

Question 33

In the z-score formula, which of the following is true if the value in the numerator is a negative value?

A) that the xi value lies to the left of the mean
B) that the mean is of lesser value than the xi value
C) that the mean is of negative value
D) that the numerator value cannot be divided by the standard deviation

Question 34

Which of the following cases require the mean of a sample to be calculated using the formula $\bar { x } = \frac { \sum _ { i = 1 } ^ { N } f _ { i } x _ { i } } { N }$ , where N represents the sample size?

A) the sample has no mode value
B) there is direct access to the raw data
C) sample data are grouped in a frequency distribution
D) the coefficient of skewness is 1 or less than -1

Question 35

Calculate the coefficient of variation from the following data: z-score = 1.32; standard deviation = 0.173; mean = 4.7; total variation = 0.6

A) 27.16
B) 156.66
C) 0.04
D) -0.5

Question 36

In statistics, refers to the peakedness or flatness of a histogram.

A) Sharpe ratio
B) entropy rate
C) Markov chain
D) kurtosis

Question 37

Which of the following is the equation for calculating the coefficient of variation (CV)?

A) CV = standard deviation/mean
B) CV = standard deviation - z-score/mean (total variation)
C) CV = value of observation's distance from mean/standard deviation
D) CV = mean/(standard deviation)2

Question 38

Which of the following values of the coefficients of variation of stocks represents the least risky stock?

A) 1.0
B) 0.005
C) 0.5
D) 0.045

Question 39

Which of the following describes standard deviation?

A) It is the average of the greatest and least values in the data set.
B) It is the square root of the variance.
C) It is the difference between the first and third quartiles of a data set.
D) It is the average of the squared deviations of the observations from the mean.

Question 40

A z-score of 1.0 means that .

A) the observation is -1.0 standard deviation to the right of the mean
B) the observation is -1.0 standard deviation to the left of the mean
C) the observation has no deviation from the mean
D) the observation is 1.0 standard deviation to the right of the mean

Question 41

For an odd number of observations, the median is the mean of the two middle numbers.

Question 42

Below is the data collected from a manufacturing process for a part whose dimensions are specified as 4.00 ± 0.1 centimeters. Calculate the process capability index within three standard deviations of the mean.

Question 43

Compare and contrast methods of summarizing and describing data
Use the spreadsheet below to answer the following question(s).
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y). $$\begin{array}{l}\begin{array} { | l | l | } \hline\text { Shoes sold }\\ \text { in \% (X) } & \text { Price (Y) } \\\hline 15 & \$ 48 \\\hline 27 & \$ 55 \\\hline 10 & \$ 40 \\\hline 13 & \$ 88 \\\hline 25 & \$ 53 \\\hline 9 & \$ 47 \\\hline 18 & \$ 40 \\\hline & \\\hline\end{array}\end{array}$$

-Use Excel to calculate the variance of X.

A) 271.33
B) 16.47
C) 49.57
D) 7.04

Question 44

One of the properties of the mean is that the sum of the deviations of each observation from the mean is zero.

Question 45

Calculate the standard deviation for cost per order in the following table.

Question 46

Which of the following is true of covariance, between two variables, when one of the deviations from the mean is positive and the other is negative?

A) the degree of linear association is high between the two variables
B) there is no covariance between the two variables
C) the covariance will be negative
D) the covariance will be positive

Question 47

is a measure of the linear relationship between two variables, X and Y, which does not depend on the units of measurement.

A) Kurtosis
B) Proportion
C) Skewness
D) Correlation

Question 48

A sample is a subset of a population.

Question 49

Compare and contrast methods of summarizing and describing data
Use the spreadsheet below to answer the following question(s).
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y). $$\begin{array}{l}\begin{array} { | l | l | } \hline\text { Shoes sold }\\ \text { in \% (X) } & \text { Price (Y) } \\\hline 15 & \$ 48 \\\hline 27 & \$ 55 \\\hline 10 & \$ 40 \\\hline 13 & \$ 88 \\\hline 25 & \$ 53 \\\hline 9 & \$ 47 \\\hline 18 & \$ 40 \\\hline & \\\hline\end{array}\end{array}$$

-Use Excel to calculate the mean for X.

A) 16.71
B) 7.04
C) 2.67
D) 0.02

Question 50

Compare and contrast methods of summarizing and describing data
Use the spreadsheet below to answer the following question(s).
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y). $$\begin{array}{l}\begin{array} { | l | l | } \hline\text { Shoes sold }\\ \text { in \% (X) } & \text { Price (Y) } \\\hline 15 & \$ 48 \\\hline 27 & \$ 55 \\\hline 10 & \$ 40 \\\hline 13 & \$ 88 \\\hline 25 & \$ 53 \\\hline 9 & \$ 47 \\\hline 18 & \$ 40 \\\hline & \\\hline\end{array}\end{array}$$

-Use Excel to calculate the standard deviation for Y.

A) 49.57
B) 16.47
C) 7.04
D) 2.6

Question 51

The following table lists the amounts paid in mortgages as a percentage of the household income in the town Aponia. Calculate the variance and standard deviation of the data, if mean is given as 22.4%. The percentage (x) values are estimated as midpoints of each percentage range.

Question 52

Compare and contrast methods of summarizing and describing data
Use the spreadsheet below to answer the following question(s).
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y). $$\begin{array}{l}\begin{array} { | l | l | } \hline\text { Shoes sold }\\ \text { in \% (X) } & \text { Price (Y) } \\\hline 15 & \$ 48 \\\hline 27 & \$ 55 \\\hline 10 & \$ 40 \\\hline 13 & \$ 88 \\\hline 25 & \$ 53 \\\hline 9 & \$ 47 \\\hline 18 & \$ 40 \\\hline & \\\hline\end{array}\end{array}$$

-Use Excel to calculate the z-score of X observation 27.

A) -0.24
B) 0
C) 0.18
D) 1.46

Question 53

Compare and contrast methods of summarizing and describing data
Use the spreadsheet below to answer the following question(s).
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y). $$\begin{array}{l}\begin{array} { | l | l | } \hline\text { Shoes sold }\\ \text { in \% (X) } & \text { Price (Y) } \\\hline 15 & \$ 48 \\\hline 27 & \$ 55 \\\hline 10 & \$ 40 \\\hline 13 & \$ 88 \\\hline 25 & \$ 53 \\\hline 9 & \$ 47 \\\hline 18 & \$ 40 \\\hline & \\\hline\end{array}\end{array}$$

-Use Excel to calculate the correlation between variables X and Y.

A) 16.47
B) 0.02
C) 16.71
D) 7.04

Question 54

The table below shows the sales per day at a grocery store over a period of a week. Calculate the z-score for sales on Day 4.

Question 55

Compare and contrast methods of summarizing and describing data
Use the spreadsheet below to answer the following question(s).
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y). $$\begin{array}{l}\begin{array} { | l | l | } \hline\text { Shoes sold }\\ \text { in \% (X) } & \text { Price (Y) } \\\hline 15 & \$ 48 \\\hline 27 & \$ 55 \\\hline 10 & \$ 40 \\\hline 13 & \$ 88 \\\hline 25 & \$ 53 \\\hline 9 & \$ 47 \\\hline 18 & \$ 40 \\\hline & \\\hline\end{array}\end{array}$$

-Use Excel to calculate the covariance between variables X and Y.

A) 2.67
B) 0.02
C) 16.71
D) 7.04

Question 56

Compare and contrast methods of summarizing and describing data
Use the spreadsheet below to answer the following question(s).
Below is the table showing rate of shoes sold per day and the highest-priced shoe sold that day for a one-week period. The rate of shoes sold per day (X) and the price of the shoes (Y). $$\begin{array}{l}\begin{array} { | l | l | } \hline\text { Shoes sold }\\ \text { in \% (X) } & \text { Price (Y) } \\\hline 15 & \$ 48 \\\hline 27 & \$ 55 \\\hline 10 & \$ 40 \\\hline 13 & \$ 88 \\\hline 25 & \$ 53 \\\hline 9 & \$ 47 \\\hline 18 & \$ 40 \\\hline & \\\hline\end{array}\end{array}$$

-Use Excel to calculate the coefficient of variation of X.

A) 0.42
B) 0.31
C) 7.04
D) 16.47

Question 57

For two variables, a positive correlation coefficient indicates .

A) a linear relationship exists for which one variable increases as the other also increases
B) a linear relationship exists for one variable that increases while the other decreases
C) that the two variables have no linear relationship with each other
D) a nonlinear relationship with no linear correlation between the two variables

Question 58

The table below shows the daily frequency of female customers at a particular ice cream shop during discount sale periods. The data is collected for 5 days. Calculate the mean for the data.

Question 59

Which of the following is the equation used for computing the sample correlation coefficient?

Question 60

Which of the following formula is used to compute covariance between two variables X and Y?

Question 61

Two variables can only have a statistical relationship if there is a cause-and-effect factor between them.

Question 62

What is statistical thinking? How is it important to making business decisions?

Question 63

Skewness describes the lack of symmetry of data.

Question 64

What are the different interpretations for correlation coefficient values?

Question 65

According to the interquartile range, extreme outliers are more than 3*IQR away from the left of Q1 or to the right of Q3.

Question 66

Give an account of Excel's Descriptive Statistics Tool.

Question 67

The value of a coefficient of skewness falling between 0.5 and -0.5 indicates relative symmetry.

Question 68

If the distribution of observations are such that mode < median < mean, the histogram would be said to be negatively skewed.

Question 69

Two different sets of data can never have the same z-scores.

Question 70

In stock trading, the higher the coefficient of variation for the stock, the smaller the relative risk is for the return provided.

Question 71

How can outliers be identified in a data set?

Question 72

State the three empirical rules in standard deviation.

Question 73

A correlation of 0 indicates that the two variables have no linear relationship with each other.

Question 74

According to the empirical rules of standard deviation in statistics, approximately 68% of the observations will fall within three standard deviations of the mean.

Question 75

The larger the variance, the more the data are spread out from the mean.