Chapter 3 - Numerical Descriptive Measures

In a neighborhood there are five houses listed for sale for the following amounts: $250,000; $275,000; $280,000; $295,000; and $515,000. What is the BEST measure of central location for the price of a house in the neighborhood? Mode Arithmetic mean Geometric mean Median

Median

population size

N

Correlation

correl (array1, array2)

Sample covariance

covariance (array1, array2)

Kurtosis

kurt (array)

A negative skewness coefficient implies that extreme observations are concentrated in the _ tail of the distribution

left

Maximum

max(df$var)

Mean

mean(df$var)

The notation s2 represents the sample variance. sample standard deviation. population variance. population standard deviation.

sample variance

Skewness

skew (array)

Multiple measures

summary(df)

The function to find the mean of a subset in R is

tapply

The range is the difference between the largest and the smallest values. the first and the third quartiles. the mean and the median.

the largest and the smallest values.

When there are an odd number of observations, and the observations are in order from smallest to largest, the median is... The average of the two middle observations The last observation The middle observation Average of the first and last observation. The first observation

the middle observation

Two widely used measures of dispersion are... the mean and the median. the mean absolute deviation and the mode. the variance and the standard deviation. the mode and the range.

the variance and the standard deviation.

The mode's usefulness as a measure of central location tends to diminish with variables that have more than _ modes.

three

A _ mean is used to calculate the mean of a frequency distribution.

weighted

sample mean symbol

x̅

sample mean formula

x̅ = ∑i=1nxin

population mean

μ

population standard deviation

σ

popular variance

σ2

The _ _ term relates to the way data tend to cluster around some middle or central value.

central location

The arithmetic mean is usually NOT a good measure of central location if a(n) ______ exists.

outlier

The _ is not considered a good measure of dispersion because it focuses solely on the extreme values and ignores every other observation in the sample or the population.

range

The first step to determine the median is to find the range of the data set find the average of the data set. place the data in numerical order.

place the data in numerical order.

The mean is usually greater than the median when the data are _ skewed.

positive

Percentile

quantile(df$var, p)

What is the most widely-used measure of central location? Mean Mode Range Variance

Mean

A skewness coefficient of _ indicates the observations are evenly distributed on both sides of the mean.

0

What is the most widely-used measure of central location? Variance Range Mean Mode

Mean

In which of the following data sets would the arithmetic mean NOT be a good measure of central location? 2, 3, 4, 4, 5 6, 7, 7, 8, 8 7, 8, 8, 9, 25 5, 5, 6, 6, 7

7, 8, 8, 9, 25

Which of the following statements about the mean absolute deviation (MAD) is MOST accurate? MAD is the square root of the standard deviation. MAD can be a positive number or a negative number. MAD is denominated in the same units as the original data. MAD is the arithmetic mean of the squared deviations from the mean.

MAD is denominated in the same units as the original data.

When there are an even number of observations, and the observations are in order from smallest to largest, the median is...

The average of the two middle observations

When there are an even number of observations, and the observations are in order from smallest to largest, the median is... Average of the first and last observation. The last observation The average of the two middle observations The middle observation The first observation

The average of the two middle observations

A researcher wants to compare the variability of two data sets that have different units of measurement. Which of the following measures is MOST useful as a relative measure of dispersion? The coefficient of variation The range The standard deviation The variance

The coefficient of variation

The formula for the weighted mean is xx=Σwixi. Using this formula, what is the restrictions on the weights. They must some to n for a sample and N for a population. They must sum to zero. They must sum to one. There are no restrictions.

They must sum to one.

True or false: The mean is the most widely used measure of central location for quantitative data.

True

Which of the following is not a measure of central location? Variance Mean Weighted mean Median

Variance

The function to find the mean of a subset in Excel is .

averageif

Generally, the _ is the best measure of central location when outliers are present.

median

The measure of central location where half the values of the data set lie above this measure and half the values of the data set lie below this measure is known as the ______. outlier median mode mean

median

Median

median(df$var)

Minimum

min(df$var)

An owner of a grocery store wants to determine the brands of soda that customers purchase at the store. When summarizing the data about soda brand purchases, the meaningful measure of central location is the ______. variance mean mode median

mode

The ______ is a measure of central location that is the most frequently occurring value in the data set. median range mean mode

mode

When summarizing a qualitative data set, the ______ is the best measure of central location. variance standard deviation mode median

mode

sample size

n