Deck 2: Descriptive Statistics

Question 1

The data on grades (A, B, C, and D) scored by all students in a test is an example of

A) quantitative datA)
B) sample data.
C) categorical data.
D) analytical data.

Answer 1

categorical data.

Question 2

A variable whose values are not known with certainty is called a _____.

A) certain variable
B) random variable
C) constant variable
D) decision variable

Answer 2

random variable

Question 3

The act of collecting data that are representative of the population data is called

A) random sampling.
B) sample data.
C) population sampling.
D) applications of business analytics.

Answer 3

random sampling.

Question 4

_____ are collected from several entities at the same point in time.

A) Time series data
B) Categorical and quantitative data
C) Cross-sectional data
D) Random data

Question 5

The difference in a variable measured over observations (time, customers, items, etc.) is called as _____.

A) observed differences
B) variation
C) variable change
D) descriptive analytics

Question 6

A set of values corresponding to a set of variables is defined as a(n) _____.

A) quantity
B) event
C) factor
D) observation

Question 7

A variable is defined as a

A) quantity of interest that can take on same values.
B) set of values.
C) quantity of interest that can take on different values.
D) characteristic that takes on same values from a set of values.

Question 8

_____ act(s) as a representative of the population.

A) The analytics
B) The variance
C) A sample
D) The random variables

Question 9

The data collected from the customers in restaurants about the quality of food is an example of

A) variable study.
B) cross-sectional study.
C) experimental study.
D) observational study.

Question 10

In a(n) _____, one or more variables are identified and controlled or manipulated so that data can be obtained about how they influence the variable of interest identified first.

A) experimental study
B) observational study
C) categorical study
D) variable study

Question 11

A summary of data that shows the number of observations in each of several nonoverlapping bins is called

A) a frequency distribution.
B) a sample summary.
C) a bin distribution.
D) an observed distribution.

Question 12

Which of the following are necessary to be determined to define the classes for a frequency distribution with quantitative data?

A) Number of nonoverlapping bins, width of each bin, and bin limits
B) Width of each bin and bin lower limits
C) Number of overlapping bins, width of each bin, and bin upper limits
D) Width of each bin and number of bins

Question 13

Consider the data below. What percentage of students scored grade C?

A) 33%
B) 31%
C) 37%
D) 28%

Question 14

The purpose of using enough bins is to show the

A) number of observations.
B) number of variables.
C) variation in the data.
D) correlation in the data.

Question 15

Data collected from several entities over several time periods is

A) categorical and quantitative datA)
B) time series data.
C) source data.
D) cross-sectional data.

Question 16

When the data are large and when it is difficult to analyze all at once, which of the following feature in Excel is used to make the data more manageable and to develop insights?

A) Frequency table
B) Sorting and filtering
C) Fill color
D) Charts

Question 17

Which of the following gives the proportion of items in each bin?

A) Frequency
B) Percent frequency
C) Relative frequency
D) Bin proportion

Question 18

The data on the time taken by₁₀ students in a class to answer a test is an example of

A) population datA)
B) categorical data.
C) time series data.
D) quantitative data.

Question 19

_____ provide facts and figures that can be used for analysis and interpretation of a population of interest.

A) Data
B) Variables
C) Range
D) Query

Question 20

Compute the relative frequencies for the data given in the table below:

A) 0.31, 0.14, 0.37, 0.18
B) 0.37, 0.14, 0.31, 0.18
C) 0.14, 0.31, 0.37, 0.18
D) 0.18, 0.31, 0.37, 0.14

Question 21

Compute the standard deviation for the following sample data. 32 41 36 24 29 30 40 22 25 37

A) 5.96
B) 6.41
C) 5.42
D) 6.75

Question 22

Any data value with a z-score less than -3 or greater than +3 is treated as a(n)

A) outlier.
B) usual value.
C) whisker.
D) z-score value.

Question 23

The variance is based on the

A) deviation about the median.
B) number of variables.
C) deviation about the mean.
D) correlation in the data.

Question 24

Compute the mode for the following data: 12 16 19 10 12 11 21 12 21 10

A) 21
B) 11
C) 12
D) 10

Question 25

The simplest measure of variability is the

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

Question 26

Compute the geometric mean for the following data on growth factors of an investment for 10 years: 1.10 0.50 0.70 1.21 1.25 1.12 1.16 1.11 1.13 1.22

A) 1.0221
B) 1.0148
C) 1.0363
D) 1.1475

Question 27

Compute the 50th percentile for the following data: 10 15 17 21 25 12 16 11 13 22

A) 18.6
B) 13.3
C) 15.5
D) 17.7

Question 28

Compute the third quartile for the following data. 10 15 17 21 25 12 16 11 13 22

A) 21.25
B) 15.5
C) 21.5
D) 11.75

Question 29

Compute IQR for the following data. 10 15 17 21 25 12 16 11 13 22

A) 6.25
B) 7.75
C) 5.14
D) 9.50

Question 30

The _____ shows the number of data items with values less than or equal to the upper class limit of each class.

A) cumulative frequency distribution
B) frequency distribution
C) percent frequency distribution
D) relative frequency distribution

Question 31

Compute the mean of the following data: 56 42 37 29 45 51 30 25 34 57

A) 42.8
B) 52.1
C) 40.6
D) 39.4

Question 32

Identify the shape of the distribution in the below figure.

A) Moderately skewed left
B) Symmetric
C) Highly skewed right
D) Moderately skewed right

Question 33

For the following sample data, compute the variance. 32 41 36 24 29 30 40 22 25 37

A) 45.6
B) 35.5
C) 41.04
D) 29.4

Question 34

A _____ determines how far a particular value is from the mean relative to the data set's standard deviation.

A) coefficient of variation
B) z-score
C) variance
D) percentile

Question 35

Compute the median of the following data: 32 41 36 24 29 30 40 22 25 37

A) 28
B) 31
C) 40
D) 34

Question 36

Which of the following graphs provide information on outliers and IQR of a data set?

A) Histogram
B) Line chart
C) Scatter chart
D) Box plot

Question 37

_____ is a graphical summary of data previously summarized in a frequency distribution.

A) Box plot
B) Histogram
C) Line chart
D) Scatter chart

Question 38

The _____ is a point estimate of the population mean for the variable of interest.

A) sample mean
B) median
C) Sample
D) geometric mean

Question 39

For data having a bell-shaped distribution, approximately _____ percent of the data values will be within one standard deviation of the mean.

A) 95
B) 66
C) 68
D) 97

Question 40

Compute the coefficient of variation for the following sample data. 32 41 36 24 29 30 40 22 25 37

A) 18.64 percent
B) 21.36 percent
C) 20.28 percent
D) 21.67 percent

Question 41

Consider a sample on the waiting times (in minutes) at the billing counter in a grocery store to be 15, 24, 18, 15, 21, 20, 15, 22, 19, 16, 15, 22, 20, 15, and 21. Compute the 25th, 50th, and 75th percentiles.

Question 42

Consider a sample on the waiting times (in minutes), at the billing counter in a grocery store, to be 15, 24, 18, 15, 21, 20, 15, 22, 19, 16, 15, 22, 20, 15, and 21. Compute the mean, median, and mode.

Question 43

The partial relative frequency distribution is given below:

a. What is the relative frequency of group 4?
b. The total sample size is 400. What is the frequency of group 4?
c. Show the frequency distribution.
d. Show the percent frequency distribution.

Question 44

Suppose that the average time an employee takes to reach the office is 35 minutes. To address the issue of late comers, the mode of transport chosen by the employee is tracked: private transport (two-wheelers and four-wheelers) and public transport. The data on the average time (in minutes) taken using both a private transportation system and a public transportation system for a sample of employees are given below:

a. Considering the travel times (in minutes) of employees using private transport. Compute the z-score for the tenth employee with travel time of 29 minutes.
b. Considering the travel times (in minutes) of employees using public transport. Compute the z-score for the second employee with travel time of 29 minutes. How does this z-score compare with the z-score you calculated for part a?
c. Based on z-scores, do the data for employees using private transport and public transport contain any outliers?

Question 45

The results of a survey showed that on average, children spend 5.6 hours at PlayStation per week. Suppose that the standard deviation is 1.7 hours and that the number of hours at PlayStation follows a bell-shaped distribution.
a. Use the empirical rule to calculate the percentage of children who spend between 2.2 and 9 hours at PlayStation per week.
b. What is the z-value for a child who spends 7.5 hours at PlayStation per week?
c. What is the z-value for a child who spends 4.5 hours at PlayStation per week?

Question 46

The following table provides information on the number of billionaires in a country and the continents on which these countries are located.
a. Sort the countries from largest to smallest based on the number of billionaires. What are the top 5 countries according to the number of billionaires? b. Filter the countries to display only the countries located in North America.

Question 47

If covariance between two variables is near 0, then it implies that

A) there exists a positive relationship between the variables.
B) the variables are not linearly related.
C) the variables are negatively related.
D) the variables are strongly relateD)

Question 48

Suppose that you make a fixed deposit of $1,000 in Bank X, and $500 in Bank Y. The value of each investment at the end of each subsequent year is provided in the table:

Which of the two banks provide a better return over this time period?

Question 49

The manager of an automobile showroom studied the time spent by each salesman interacting with the customer in a month apart from the other jobs assigned to them. The data in hours are given below.

Using classes 1013, 1417, and so on, show: Using classes 10-13, 14-17, and so on, show:
The frequency distribution.
The relative frequency distribution.
The cumulative frequency distribution.
The cumulative relative frequency distribution.
The proportion of salesmen who spend 13 hours of time or less with the customers.
Prepare a histogram and comment on the shape of the distribution.

Question 50

A survey on the most preferred newspaper in USA listed The New York Times(TNYT), Washington Post(WP), Daily News(DN), New York Post(NYP), and Los Angeles Times (LAT) as the top five most preferred newspapers. The table below shows the preferences of 50 citizens.

a. Are these data categorical or quantitative?
b. Provide frequency and percent frequency distributions.
c. On the basis of the sample, which newspaper is preferred the most?

Question 51

Suppose that the average time an employee takes to reach the office is 35 minutes. To address the issue of late comers, the mode of transport chosen by the employee is tracked: private transport (two-wheelers and four-wheelers) and public transport. The data on the average time (in minutes) taken using both a private transportation system and a public transportation system for a sample of employees are given below:

a. What are the mean and median travel times for employees using a private transport? What are the mean and median travel times for employees using a public transport?
b. What are the variance and standard deviation of travel times for employees using a private transport? What are the variance and standard deviation of travel times for employees using a public transport?
c. Comment.

Question 52

A student willing to participate in a debate competition required to fill a registration form. State whether each of the following information about the participant provides categorical or quantitative data.
a. What is your date of birth?
b. Have you participated in any debate competition previously?
c. If yes, how many debate competitions have you participated so far?
d. Have you won any of the competitions?
e. If yes, how many have you won?

Question 53

The average time a customer service executive takes to resolve an issue on a mobile handset is 26.4 minutes. The average time taken to resolve the issue by a sample of 15 such executives are shown below:

a. What is the mean resolution time?
b. What is the median resolution time?
c. What is the mode for these 15 executives?
d. What is the variance and standard deviation?
e. What is the third quartile?

Question 54

The scores of a sample of students in a Math test are 20, 15, 19, 21, 22, 12, 17, 14, 24, 16 and in a Stat test are 16, 12, 19, 17, 22, 14, 20, 21, 24, 15, 13.
a. Compute the mean and median scores for both the Math and the Stat tests.
b. Compare the mean and median scores computed in part a. Comment.

Question 55

The mentor of a class researched on the number of hours spent on study in a week by each student of the class, to analyze the correlation between the study hours and the marks obtained by each student. The data on the hours spent per week by 25 students are listed below:

a. What is the least amount of time a student spent per week on studying after school hours in this sample? The highest?
b. Use a class width of 2 hours to prepare a frequency distribution, a relative frequency distribution, and a percent frequency distribution for the data.
c. Prepare a histogram and comment on the shape of the distribution.

Question 56

Eight observations taken for two variables are as follows:

a. Develop a scatter diagram with x on the horizontal axis.
b. What does the scatter diagram developed in part a indicate about the relationship between the two variables?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.

Question 57

The data on the percentage of visitors in the previous and current years at 12 well-known national parks of Unites States are given below:

a. Sort the parks in descending order by their current year's visitor percentage. Which park has the highest number of visitors in the current year? Which park has the lowest number of visitors in the current year?
b. Calculate the change in visitor percentage from the previous to the current year for each park. Use Excel's conditional formatting to highlight the park whose visitor percentage decreased from the previous year to the current year.
c. Use Excel's conditional formatting tool to create data bars for the change in visitor percentage from the previous year to the current year for each park calculated in part b.

Question 58

A study on the average minutes spent by students on internet usage is 300 with a standard deviation of 102. Answer the following questions assuming a bell-shaped distribution and using the empirical rule.
a. What percentage of students use internet for more than 402 minutes?
b. What percentage of students use internet for more than 504 minutes?
c. What percentage of students use internet between 198 minutes and 300 minutes?

Question 59

The correlation coefficient will always take values

A) greater than 0.
B) between -1 and 0.
C) between -1 and +1.
D) less than -1.

Question 60

Consider the following data on income and savings of a sample of residents in a locality:

a. Compute the correlation coefficient. Is there a positive correlation between the income and savings? What is your interpretation?
b. Show a scatter diagram of the relationship between the income and savings.