Deck 3: Descriptive Statistics: Numerical Methods

Question 1

The median is the value below which and above which approximately 50 percent of the measurements lie.

Answer 1

True

Question 2

If there are seven classes in a frequency distribution,then the fourth class will always contain the median.

Answer 2

False

Question 3

In a symmetric population,the median equals the mode.

Answer 3

True

Question 4

The line that minimizes the sum of the squared horizontal (x)distances between the points on the scatter plot and the line is the least squares line.

Question 5

The mode is the measurement in a sample or population that occurs most frequently.

Question 6

Range is a better measure of variation than standard deviation.

Question 7

The weights that are used in calculating a weighted mean will vary depending on the situation.

Question 8

The median is the measure of central tendency that divides a population or sample into four equal parts.

Question 9

The mean is one component of the five-number summary.

Question 10

The range of the measurement is the largest measurement plus the smallest measurement.

Question 11

The population mean is the point estimate of the sample mean.

Question 12

It is appropriate to use the Empirical Rule to describe a population that is extremely skewed.

Question 13

The population mean is the average of the population measurements.

Question 14

Chebyshev's Theorem is only of practical use when analyzing a non-mound-shaped population that is not very skewed.

Question 15

The median is said to be resistant to extreme values.

Question 16

The population variance is the average of the squared deviations of the individual population measurements from the population mean.

Question 17

The pth percentile is a value such that (100−p)percent of the measurements fall at or below the value.

Question 18

Z-score is often used as a measure of risk.

Question 19

Data summarized in a frequency distribution or histogram form are often called weighted data.

Question 20

A correlation coefficient close to −1 says x and y are highly related.

Question 21

In the calculation of a mean for grouped data,we assume that the average of the measurements in each class equals the class midpoint.

Question 22

The average of the squared deviations of the individual population measurement from the population mean is the ___________.

A) standard deviation
B) mean
C) variance
D) median
E) range

Question 23

If the mean is greater than the median,then the distribution is ___________.

A) skewed right
B) skewed left
C) symmetrical
D) bimodal

Question 24

The measurement in a sample or a population that occurs most frequently is the ___________.

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

Question 25

The geometric mean is the rate of change that yields better wealth at the end of a set of time periods than the actual returns.

Question 26

A measurement located outside the upper limits of a box-and-whiskers display is ___________.

A) always in the first quartile
B) an outlier
C) always the largest value in the data set
D) within the lower limits

Question 27

When using Chebyshev'sTheorem to obtain the bounds for 99.73 percent of the values in a population,the interval generally will be ___________ the interval obtained for the same percentage if a normal distribution is assumed (Empirical Rule).

A) shorter than
B) wider than
C) the same as

Question 28

If the mean,median,and mode for a given population all equal 25,then we know that the shape of the distribution of the population is ____________.

A) bimodal
B) skewed to the right
C) symmetrical
D) skewed to the left

Question 29

A disadvantage of using grouping (a frequency table)with sample data is that

A) calculations involving central tendency and variation are more complicated than central tendency and variation calculations based on ungrouped data.
B) the descriptive statistics are less precise than the descriptive statistics obtained using ungrouped data.
C) the interpretation of the grouped data descriptive statistics is meaningless.
D) it is much more difficult to summarize the information than it is with the ungrouped data.

Question 30

Another name for the 50th percentile is the ___________.

A) mean
B) first quartile
C) median
D) mode
E) third quartile

Question 31

A quantity that measures the variation of a population or a sample relative to its mean is called the ____________.

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

Question 32

Which percentile describes the third quartile,Q3?

A) 25th
B) 50th
C) 75th
D) 100th

Question 33

As a measure of variation,the sample ___________ is easy to understand and compute.It is based on the two extreme values and is therefore a highly unstable measure.

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

Question 34

Which percentile describes the first quartile,Q1?

A) 25th
B) 50th
C) 75th
D) 100th

Question 35

The ending value of an initial investment can be calculated using weighted means.

Question 36

If a population distribution is skewed to the right,then,given a random sample from that population,one would expect that the ____________.

A) median would be greater than the mean
B) mode would be equal to the mean
C) median would be less than the mean
D) median would be equal to the mean

Question 37

All of the following are measures of central tendency except the ____________.

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

Question 38

Which of the following is influenced the least by the occurrence of extreme values in a sample?

A) mean
B) median
C) geometric mean
D) weighted mean

Question 39

When calculating the geometric mean,a quantity of 1 is added to the nth root of the product (1 + R₁)(1 + R₂)...(1 + R_n).

Question 40

A normal population has 99.73 percent of the population measurements within __________ standard deviation(s)of the mean.

A) 1
B) 2
C) 3
D) 4

Question 41

A company CEO asked the marketing research department to find the average age of consumers who bought the most profitable product made by the company.From survey data gathered two years ago,the researchers found the following table.Calculate the average age to give to the CEO.

Question 42

Find the weighted mean per capita income for the following random sample of six cities in the Midwest.

Question 43

Following a factor analysis of 15 personality characteristic ratings of politicians by a random sample of 40,000 registered voters,the following table of the first 7 factors and their corresponding eigenvalues and percentage of explained variation was produced.Which factors should an analyst choose when defining the characteristics of politicians?

Question 44

The geometric mean growth rate of sales for used cars in a geographic area from 2005 to 2009 was 16.42 percent.Annual sales in 2005 were $14.2 million.Find the ending value of sales after this four-year period.

Question 45

At the end of 2007,the IRA owned by Joe Smith had a value of $1.2 million.With a rate of return of −29.75 percent in 2008 and a rate of return of 2.98 percent in 2009,calculate the geometric mean rate of return for the two-year period.

Question 46

A manufacturer of Product X has developed a model for predicting monthly sales of their product based on the sales from the same month of the previous year and the forecasted average daily temperature for the month.Using the regression tree below based on a random sample of 30 observations,predict sales for a future where the previous year's monthly sales were $15 million dollars and the forecasted average daily temperature for the month will be 45 degrees.

Question 47

An interval that contains a specified percentage of the individual measurements is called a(n)_______________ interval.

A) three-sigma
B) tolerance
C) normal
D) empirical

Question 48

An initial investment of $10,000 has a value of $7,382 at the end of year 1.What is the rate of return for the first year?

Question 49

Suppose that annual sales for a company were $3.6 million at the beginning of a three-year period and at the end had increased to $6.1 million.Find the geometric growth rate of sales.

Question 50

An initial investment of $10,000 is observed over 3 years with a geometric mean return at the end of year 3 of 0.512.Determine the value of the investment after 3 years.

Question 51

A local grocery market is studying whether to offer a loyalty program to its customers.In its final analyses the following groups are being used to categorize loyalty card customers: family income and number of children.Using the classification tree below,estimate the percentage of customers with an income of $50,000 with 2 children who would use a loyalty card

Question 52

The point estimate of the _______________ is the positive square root of the sample variance.

A) sample mean
B) sample standard deviation
C) range
D) median
E) population standard deviation

Question 53

Which of the following is a measure of the strength of the linear relationship between x and y that is dependent on the units in which x and y are measured.

A) covariance
B) correlation coefficient
C) slope
D) least squares line

Question 54

The ______________ is a quantity that measures the variation of a population or sample relative to its mean.

A) mean
B) standard deviation
C) range
D) coefficient of variation
E) Z-score

Question 55

A manufacturer of Product X has developed a model for predicting monthly sales of their product based on the sales from the same month of the previous year and the forecasted average daily temperature for the month.Using the regression tree below based on a random sample of 30 observations predict sales for a future where the previous year's monthly sales were $21.2 million dollars and the forecasted average daily temperature for the month will be 45 degrees.

Question 56

As the coefficient of variation _______________,risk ______________.

A) increases,decreases
B) decreases,increases
C) increases,increases
D) remains constant,increases

Question 57

The rate of return for each of the past four years on a market fund are R₁ = 2.4%,R₂ = 1.0%,R₃ = −3.2%,and R₄ = 0.5%.Find the geometric mean rate of return.