Question 1

In an extremely right-skewed distribution,the mean is less than the median.

Accepted Answer

In an extremely right-skewed distribution, the mean is typically greater than the median because the long tail to the right pulls the mean higher.

Question 2

Because they represent such extreme values,outliers should always be eliminated from statistical analyses.

Accepted Answer

Outliers should not always be eliminated because they can represent valuable variations in the data or indicate errors or anomalies that are important for the analysis. Removing them without careful consideration can lead to biased results.

Question 3

The core purpose of time series graphs is to detect historical patterns in the data.

Accepted Answer

Time series graphs are used to visualize data points over a period of time, allowing for the identification of trends, patterns, and fluctuations in the data, which is essential for understanding historical behavior and making forecasts.

Question 4

The value of the mean times the number of observations equals the sum of all of the data values.

Accepted Answer

The mean is calculated as the sum of all data values divided by the number of observations, so multiplying the mean by the number of observations gives the sum of all data values.

Question 5

If a histogram of a data set is symmetric and bell shaped,with a mean of 75 and standard deviation of 10.Then,approximately 95% of the data values will be between 55 and 95.

Accepted Answer

This follows the empirical rule (68-95-99.7 rule) for a normal distribution, where approximately 95% of the data falls within two standard deviations of the mean. Here, two standard deviations from the mean (75) are 75 ± 2(10) = 55 to 95.

Question 6

A histogram is based on binning the variable,which means putting the values of the numeric variable into discrete categories.

Accepted Answer

A histogram groups numbers into ranges (bins) and is used for the distribution of a continuous data variable, effectively putting values into discrete categories based on those ranges.

Question 7

In order for the characteristics of a sample to be generalized to the entire population,the sample should be _____ the population.
A)symbolic of
B)opposite of
C)representative of
D)different from

Accepted Answer

For the characteristics of a sample to be generalized to the entire population, the sample must be representative of that population. This means the sample should accurately reflect the various segments and characteristics of the population as a whole.

Question 8

A sample of 8 observations with a sample standard deviation of 2.50 has a sample variance of 17.50.

Accepted Answer

The sample variance is the square of the sample standard deviation. Therefore, if the sample standard deviation is 2.50, the sample variance is 2.50^2 = 6.25.

Question 9

Coding males as 1 and females as 0 in a data set illustrates the use of _____ variables.
A)nominal
B)dummy
C)numerical
D)ordinal

Accepted Answer

Dummy variables are used in statistical modeling to represent categorical data with two categories, such as male or female, by coding them as 0 or 1.

Question 10

Researchers may try to gain insight into the characteristics of a population by examining a(n)_____ from the population.
A)model
B)sample
C)exemplar
D)replica

Accepted Answer

Researchers often use a sample, which is a subset of the population, to gain insights into the characteristics of the entire population without having to study every individual within it.

Question 11

Mean absolute deviation (MAD)is the average of the squared deviations.

Accepted Answer

Mean absolute deviation (MAD) is the average of the absolute deviations from a central point (mean or median), not the squared deviations. Squared deviations are used in calculating the variance.

Question 12

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

Accepted Answer

The range is defined as the difference between the maximum and minimum values in a data set, which provides a measure of the spread or dispersion of the data.

Question 13

Abby has been keeping track of what she spends to stream movies.The last seven week's expenditures,in dollars,were 6,4,8,9,6,12,and 4.The mean amount Abby spent streaming movies over these 7 weeks is $7.

Accepted Answer

To find the mean, add all expenditures together: 6 + 4 + 8 + 9 + 6 + 12 + 4 = 49. Then, divide by the number of weeks: 49 / 7 = 7.

Question 14

The mean is a measure of central tendency.

Accepted Answer

The mean, often referred to as the average, is a measure of central tendency that summarizes the central point of a data set by dividing the sum of all values by the number of values.

Question 15

Unlike histograms,box plots depict only one aspect of a variable.

Accepted Answer

Box plots provide a visual summary of the central tendency, dispersion, and skewness of a dataset, showing multiple aspects of a variable including the median, quartiles, and outliers.

Question 16

A sample,selected from a population,taken at one particular point in time is categorized as
A)categorical.
B)discrete.
C)cross-sectional.
D)time-series.

Accepted Answer

Cross-sectional data refers to data collected by observing many subjects (such as individuals, firms, countries, or regions) at the same point in time or without regard to differences in time. It provides a snapshot of a population at a single point in time, differentiating it from time-series data, which collects data from the same subjects at multiple time points.

Question 17

Gender and states of residence are examples of ____ data.
A)discrete
B)continuous
C)categorical
D)ordinal

Accepted Answer

Gender and states of residence are examples of categorical data because they describe categories or groups to which individuals or items belong, rather than numerical values.

Question 18

The median is one of the most frequently used measures of variability.

Accepted Answer

The median is a measure of central tendency, not variability. Measures of variability include the range, variance, and standard deviation.

Question 19

Time series graphs chart the values of one or more time series,using time on the vertical axis.

Accepted Answer

Time series graphs chart the values of one or more time series using time on the horizontal axis, not the vertical axis.

Question 20

There are four quartiles that divide the values in a data set into four equal parts.

Accepted Answer

There are three quartiles (Q1, Q2, Q3) that divide a data set into four equal parts.

Quiz 2: Describing the Distribution of a Variable