Stats Quiz 2

If a variable has a distribution that is bell-shaped with mean 16 and standard deviation 5, then according to the Empirical Rule, 99.7% of the data will lie between which values?

1 and 31

In​ 1994, major league baseball players went on strike. At the​ time, the average salary was​ $1,049,589, and the median salary was​ $337,500. If you were representing the​ owners, which summary would you use to convince the public that a strike was not​ needed? If you were a​ player, which would you​ use? Why was there such a large discrepancy between the mean and median​ salaries? Explain.

If you were representing the​ owners, you would use the average salary to convince the public that a strike was not needed. If you were a​ player, you would use the median salary to convince the public that a strike was needed. The average and median salaries differ so greatly because the distribution of salaries is skewed right.

True or​ False: When comparing two​ populations, the larger the standard​ deviation, the more dispersion the distribution​ has, provided that the variable of interest from the two populations has the same unit of measure.

True, because the standard deviation describes how​ far, on​ average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical​ value, and​ therefore, more dispersed.

Is the trimmed mean resistant to changes in the extreme values for the given​ data?

Yes, because changing the extreme values does not change the trimmed mean.

All the bars in a uniform distribution are

approx same height

In a statistics class, the standard deviation of the heights of all students was 3.9 inches. The standard deviation of the heights of males was 3.3 inches and the standard deviation of females was 3.2 inches. Why is the standard deviation of the entire class more than the standard deviation of males and females considered separately?

bc the distribution of the entire class has more dispersion

Classes

categories by which data are grouped

. The mean measures the

center of the​ distribution, while the standard deviation measures the spread of the distribution.

When continuous data are organized in​ tables,

data are​ categorized, or​ grouped, by intervals of numbers. Each interval represents a class

Misleading graph if

data is like 7.4, etc and you start at 7 should start at zero

class width

diff between consecutive lower class limits

Histogram depicts the higher standard​ deviation if the

distribution has more dispersion.

To determine the percentage of time a particular sum was​ observed,

divide frequency for that sum by total number of​ frequencies, that​ is, the total number of times the dice were thrown. Express the result as a percent.

ogive

graph that represents cumulative frequency or cumulative relative frequency for class

x with line on top of it > M if

histogram is skewed right

When an observation that is much larger than the rest of the data is added to a data​ set, the value of the mean will

increase.

Upper class limit

largest value within class

The distribution is skewed left if

left tail is longer than right tail

Why is the median​ resistant, but the mean is​ not?

mean is not resistant because when data are​ skewed, there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.

A statistic is resistant if it is

not sensitive to extreme values.

mode

peak of the distribution.

ogive is constructed by

plotting points whose​ x-coordinates are upper class limits and ​ y-coordinates are cumulative frequencies or cumulative relative frequencies of class. Then line segments are drawn connecting consecutive points. An additional line segment is drawn connecting first point to the horizontal axis at location representing upper limit of class that would precede first class​ (if it​ existed).

When reading an illustrated bar​ graph, the

reader needs to compare the vertical scales of each bar to see if they accurately depict the data.

For annual household incomes in a country, state whether you would expect a histogram of the data to be bell-shaped, uniform, skewed left or skewed right.

skewed right

Lower class limit

smallest value within class

standard deviation measures the

spread of the data from the mean.

In a​ stem-and-leaf plot, the

stem of a data value will consist of the digits to the left of the​ right-most digit, and the leaf will consist of the​ right-most digit. The stems are written in a vertical column in increasing​ order, a vertical line is drawn to the right of the​ stems, and each leaf corresponding to the stems is written to the right of the vertical line in ascending order. Use the legend to read the​ stem-and-leaf plot.

The mode of a variable is

the most frequent observation of the variable that occurs in the data set. To compute the​ mode, tally the number of observations that occur for each data value. The data value that occurs most often is the mode. A set of data can have no​ mode, one​ mode, or more than one mode. If no observation occurs more than​ once, the data have no mode.

Since extreme values will increase the standard deviation​ greatly,

the standard deviation cannot be a resistant measure of spread.

true or false When plotting an​ ogive, the plotted points have​ x-coordinates that are equal to the upper limits of each class.

true

True or false There is not one particular frequency distribution that is​ correct, but there are frequency distributions that are less desirable than others.

true Any correctly constructed frequency distribution is valid.​ However, some choices for categories or classes give more info about shape of distribution.

the class width on graph

width between each number on bottom of graph ex: it goes 50, 60, 70. class width is 10

ask 36 students how many times they drank in past week sampling bias?

yes bc can't get truthful answers unless anonymous

The sum of the deviations about the mean always equals

zero

for population standard deviation

don't do n-1 just n then ofc do the square root stuff

Identify the given statement as either true or false. The standard deviation can be negative.

false

Identify the given statement as either true or false. The standard deviation is a resistant measure of spread.

false

True or​ False: A data set will always have exactly one mode.

false

true or false Stem-and-leaf plots are particularly useful for large sets of data.

false

Stem-and-leaf plots

lose their usefulness when data sets are large or when consist of large range of values.

if the data set is not​ skewed, the central tendency that best describes the​ "center" of the distribution is the

mean

The standard deviation is used in conjunction with the

mean to numerically describe distributions that are bell shaped

For a distribution that is skewed​ left, which of the following is​ true?

mean < median

For a distribution that is​ symmetric, which of the following is​ true?

mean =median

For a distribution that is skewed​ right, which of the following is​ true?

mean > median

if it's symmetric

mean is best measure of central tendency

A histogram of a set of data indicates that the distribution of the data is skewed right. Which measure of central tendency will likely be​ larger, the mean or the​ median? Why?

mean will likely be larger because the extreme values in the right tail tend to pull the mean in the direction of the tail.

if distribution is skewed

median is best measure of central tendency

wider range will mean

more dispersion

median has

resistance

example Letter B represents the median because

roughly half of the values in the distribution are to the left of B and roughly half of the values in the distribution are to the right of B.

The mean is calculated by

summing all of the values and then dividing by the total number of values.

By adding a large value to the sum and only increasing the number of values by​ one,

the division will result in a larger mean.

If all observations have the same​ value,

then that value will also be the mean of the data.​ Therefore, the sum of the squared differences from the mean will be​ 0, and the standard deviation will be 0.

What is meant by the phrase degrees of freedom as it pertains to the computation of the sample standard deviation

there are n-1 degrees of freedom in the computation of s because an unknown parameter u is estimated by x with a line over it for each parameter estimated, 1 degree of freedom is lost

Why​ shouldn't classes overlap when summarizing continuous data in a frequency or relative frequency​ distribution?

Classes​ shouldn't overlap so there is no confusion as to which class observation belongs

What does it mean if a statistic is​ resistant?

Extreme values​ (very large or​ small) relative to the data do not affect its value substantially.

Over the past 10 years, five mutual funds all had the same mean rate of return. The standard deviations for each of the five mutual funds are shown below. Capital investment 8.3%. Vanity 6.2%. Global advisor 9.2%. International equities 4.6%. Nomad 7.3% Which mutual fund was least consistent in rate of return?

Global advisor

If the variance of a variable is 121 what is the standard​ deviation?

11

If the standard deviation of a variable is 9 what is the​ variance?

81

If a variable has a distribution that is bell-shaped with mean 23 and standard deviation 6, then according to the Empirical Rule, what percent of the data will lie between 5 and 41?

99.7%

The cumulative relative frequency for the last class must always be 1.​ Why?

All the observations are less than or equal to the last class

What can be said about a set of data with a standard deviation of​ 0?

All the observations are the same value.

What makes the range less desirable than the standard deviation as a measure of dispersion?

The range does not use all the observations.

True or​ False: Chebyshev's inequality applies to all distributions regardless of​ shape, but the empirical rule holds only for distributions that are bell shaped.

True, Chebyshev's inequality is less precise than the empirical​ rule, but will work for any​ distribution, while the empirical rule only works for​ bell-shaped distributions.