AP Statistics Final Exam Review

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Why is it important to look at the shape of a column of data before interpreting any statistics?

-Because shape determines the location and the spread of the column of data.
-Because graphs for shape come first in the computer output.
-To see if the data is unimodal, symmetrical, and without any exceptions.
-To see that all data values were included in the statistical analysis.

To see if the data is unimodal, symmetrical, and without any exceptions.

Why look at a chart to get shape information instead of looking at the data values themselves?

-A chart is needed to summarize the shape characteristic so that we can see it.
-Statistical computer output will give charts, but not the column of data.
-Charts are much easier to look at than columns of data.
-This statement is false, it is always better to look at the data values directly to get shape information.

A chart is needed to summarize the shape characteristic so that we can see it.

Match the two meanings below with their appropriate column titles in a frequency table.

A. Relative frequency.
B. Frequency.

-Count of the data values in a category.
-Proportion of the data values in a category.

Count of the data values in a category. : Frequency.
Proportion of the data values in a category. : Relative frequency.

In the frequency table below, what is the relative frequency for the category Mar? (answer to three decimal places, ex. 1.089)

0.156

Which of the following answers is NOT one of the first three columns in a frequency table?

-Relative Frequency
-Cumulative Frequency.
-Category.
-Frequency.

Cumulative Frequency.

In the frequency table below, what is the frequency for the category May? (answer to zero decimal places, ex. 1.)

40

In the frequency table below, what is the cumulative frequency and the cumulative relative frequency for the category Jun?

100% and 100%
160.0 and 1.0
1.0 and 1.0
35.0 and 0.21875

160.0 and 1.0

What type of graph is most appropriate to use to display the shape of qualitative data?

-A pie chart where the slices of the pie touch one each other.
-A histogram where the bars do touch each another.
-A bar chart where the bars do touch each other.
-A bar chart where the bars do not touch each other.

A bar chart where the bars do not touch each other.

A Pareto chart just a bar chart with the bars rearranged from the highest bar to the lowest bar.

TRUE or FALSE

TRUE

What type of graph is most appropriate to use to display the shape of discrete data?

-A mathematical curve such as a bell-shaped curve.
-A pie chart where the slices of the pie touch one each other.
-A bar chart where the bars do not touch each other.
-A histogram where the bars do touch each another.

A histogram where the bars do touch each another.

In a histogram for discrete data, what characteristic is shown on the x-axis, and what characteristic is shown on the y-axis?

-The data values in the data set on the x-axis, and the frequency of the data values on the y-axis.
-Bins of the data values, and bins of the frequency of the data values.
-Bins of the data values, and the frequency of the data values.
-The frequency of the data values, and the data values in the data set.

The data values in the data set on the x-axis, and the frequency of the data values on the y-axis.

In a histogram for continuous data, what characteristic is shown on the x-axis, and what characteristic is shown on the y-axis?

-The frequency of the data values, and the data values in the data set.
-Bins of the data values, and bins of the frequency of the data values.
-Bins of the data values on the x-axis, and the frequency of the data values in the bins on the y-axis.
-The data values in the data set, and the frequency of the data values.

Bins of the data values on the x-axis, and the frequency of the data values in the bins on the y-axis.

When making a histogram for continuous data, a bin is just a range of possible data values.

TRUE or FALSE

TRUE

A boxplot is used to display the shape of qualitative data.

TRUE or FALSE

FALSE

A boxplot shows location and spread information as does a histogram.

TRUE or FALSE

TRUE

In a boxplot of continuous data, what percent of the data values lie inside the box, and what percent of the data values lie outside the box?

75%, and 25%.
100%, and 0%.
25%, and 25%.
50%, and 50%.

50%, and 50%.

In the boxplot below, what is the value of the median?

10
36.25
27.5
40
17.5

27.5

In any boxplot (an example is shown below), the width of the box shows what characteristic of the data values?

-The location of the data values.
-The count of the data values.
-The spread of the data values.
-The shape of the data values.

The spread of the data values.

What is the general approach to analyzing the information in a histogram?

-First look for the mean, then look for the standard deviation.
-First look at the overall shape, then look for exceptions.
-First look at the modality, then look at the symmetry.
-First look the peak of the histogram, then look at the tails.

First look at the overall shape, then look for exceptions.

Which of the following answers is NOT one of our overall shapes?

-A symmetric shape.
-A skewed shape.
-A uniform shape.
-A modeless shape.

A modeless shape

A skewed left shape means that the peak of the histogram is on the left side of the histogram.

TRUE or FALSE

FALSE

Skewness in a histogram is a property of what in the histogram?

-The peak.
-The number of peaks.
-The tails.
-The extreme values.

The tails.

Which of the following answers is NOT an exception when analyzing a histogram?

-Any bimodal shapes.
-Any gaps or peaks.
-Any patterns or grouping
-Any extreme values.

Any bimodal shapes.

How is a gap distinguished from an extreme value?

-A gap is narrow, an extreme value is wide.
-There can be only one gap, while there can be many extreme values
-A gap is close to the peak. An extreme value is far from the peak.
-A gap is fits as part of the overall shape. An extreme value is outside the overall shape.

A gap is fits as part of the overall shape. An extreme value is outside the overall shape.

Match the appropriate set of statistics to the descriptions below.

A. Resistant statistics.
B. Efficient statistics.

-Extract the most information from a column of data.
-Less affected by extreme values.

Extract the most information from a column of data. : Efficient statistics.
Less affected by extreme values. : Resistant statistics.

Two data sets have the same size, but Data set A has a sum of squares of 97 and Data set B has a sum of squares of 197. In which data set are the data values more widely spread out?

-Data set B, because 197 can have more variation than 97.
-Data set A, because a sum of squares of 97 is smaller than a sum of squares of 197.
-Data set A, because 97 is closer to zero than 197.
-Data set B, because a sum of squares of 197 is bigger than a sum of squares of 97.

Data set B, because a sum of squares of 197 is bigger than a sum of squares of 97.

What is the formula for the sum of squares (SS)?

Sumofsquares=(x−xbar)2
Sumofsquares=(x−xbar)
Sumofsquares=∑(x)2−∑(xbar)2
Sumofsquares=∑(x−xbar)2

𝑆𝑢𝑚𝑜𝑓𝑠𝑞𝑢𝑎𝑟𝑒𝑠=∑(𝑥−𝑥𝑏𝑎𝑟)2

A deviation can never equal zero.

TRUE or FALSE

FALSE

Is the average deviation better than the standard deviation (σ)?

-No, because the standard deviation is a standardized version of the average deviation.
-Yes, because the average is the most representative value.
-No, because the average deviation always equals zero.
-Yes, because the average deviation is much quicker to calculate and much easier to use.

No, because the average deviation always equals zero.

Can the standard deviation (σ) be used to find probability?

-Yes, it can with a normal curve.
-Yes, because it is part of a distribution.
-No, because the average deviation is used.
-No, because spread is not needed to find probability.

Yes, it can with a normal curve.

What information about a data value is given by its deviation?

-The statistical distance and direction from the mean.
-The mathematical distance and direction from the mean.
-The magnitude (absolute value) of the difference between the data value and the median.
-How different the data value is from the mean and median.

The mathematical distance and direction from the mean.

A data value close to the mean has a?

Large deviation.
Small deviation.
No deviation.
Middle deviation.

Small deviation.

Match the appropriate statistic for a distribution of efficient statistics.
.
A. Histogram.
B. Standard deviation.
C. Mean.

Shape.
Location.
Spread.

Shape. : Histogram.
Location. : Mean.
Spread. : Standard deviation.

In statistics, a deviation applies to only one data value.

TRUE or FALSE

TRUE

To calculate variance, statistics does not average the deviations, instead it averages the?

The positive and negative deviations separately.
Squared deviations.
The square-root of the squared deviations.
The absolute value of the deviations.

Squared deviations

Does the sum of squares (SS) usually get bigger as more data values are added to the data set?

Yes, because there are more numbers in the data set to sum.
Yes, because bigger data sets must have bigger sum of squares than smaller data sets.
No, because the new data values could have negative squares.
No, because the sum of squares is adjusted for the number of data values in the data set.

Yes, because there are more numbers in the data set to sum.

The efficient measure of spread for a column of data is the?

Average deviation.
Standard deviation.
Middle deviation.
The average of all the deviation in the data set.

Standard deviation.

What is the statistical term for all the squared deviations added together?

Sum of squares.
Variance.
Standard deviation.
Root mean square.

Sum of squares.

Variance (σ2) is what type of measure of spread?

A raw measure of spread.
A measure of spread normalized for shape.
A measure of spread adjusted for bias.
A measure of spread standardized for the number of data values.

A measure of spread standardized for the number of data values.

A data value less than the mean has a?

Positive deviation.
Left deviation.
Negative deviation.
None of the above.

Negative deviation.

What is the appropriate denotation for variance?

φ¯ for population, v¯ for sample
μ2 for population, s2 for sample
σ2 for population, s2 for sample
VAR for population, var for sample

σ2 for population, s2 for sample

What is the appropriate denotation for standard deviation?

s population, σ for sample.
σ for population, std for sample.
µ for population, s for sample
σ for population, s for sample.

σ for population, s for sample.

The mean (µ) is NOT needed to calculate a deviation.

TRUE or FALSE

FALSE

The sum of squares (SS) is what type of measure of spread?

A standardized measure of spread.
A normalized measure of spread.
A raw measure of spread.
An adjusted measure of spread.

A raw measure of spread.

How is the sum of squares (SS) standardized into variance (σ2)?

Divide by the number of data values.
Divide by the degrees of freedom.
Take the square-root of the sum of squares.
Sum of squares is the same value as the variance.

Divide by the degrees of freedom.

Does the average deviation always equal zero for every data set?

Yes, because the deviations cluster about the mean.
Yes, because the positive and negative deviation cancel each other.
No, because this is not true.
No, because the average deviation equals zero for some data sets, but not for all datasets.

Yes, because the positive and negative deviation cancel each other.

The mean (µ) is used when thinking about the data values in a column of data because? (select two of the answers below)

The mean is easier to calculate than the median.
The mean can be used in advanced statistical methods.
A single number is easy to think about.
The mean best represents the values in the column of data.

A single number is easy to think about.
The mean best represents the values in the column of data.

Which one of the following answers is NOT correct about standard deviation?

Standarddeviation=√σ2
Standarddeviation=√Variance
Standarddeviation2=Variance−
Standarddeviation=Variance2

𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛=𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒2

A bigger standard deviation for a data set means the data values are?

Spread wider apart.
Spread narrower together.
Spread more evenly about the mean.
Have a more symmetrical spread.

Spread wider apart.

Match the appropriate statistic for a distribution of resistant statistics.

A. Boxplot.
B. Median.
C. Inter-quartile range.

Shape.
Location.
Spread.

Shape. : Boxplot.
Location. : Median.
Spread. : Inter-quartile range.

What are resistant statistics resistant to?

Any possible bias in the data values.
The presence of extreme values.
The presence of gaps in the shape .
Any minor recording errors in the data set.

The presence of extreme values.

What makes resistant statistics work?

They weight the data values lower when far from the mean.
The data values are divided by their deviation.
They look at the position of the data values, and not at their values.
They remove the high and low data values to eliminate any extreme values.

They look at the position of the data values, and not at their values.

To find resistant statistics, what must be true of the data set?

The data values must be ranked from lowest to highest.
The position of the data values must be found in the initial data set.
The data set must be checked to make certain that no two data values occupy the same position.
The data values must be ranked from highest to lowest.

The data values must be ranked from lowest to highest.

Why do positional statistics work for a data set containing extreme values?

Because extreme values occur near the mean where the positions of the data values are close together.
Because the range of position is (0, n), but the range of the values is (-∞, ∞).
Because positional statistics are not a very sensitive type of statistics.
Because in the tails, a big change in value is usually a small change in position.

Because in the tails, a big change in value is usually a small change in position.

Percentiles are NOT positional statistics.

TRUE or FALSE

FALSE

When denoting a percentile (Pk) what does the k stand for?

The percentage of data values greater than (to the right of) the percentile.
This is archaic nomenclature, now k is no longer used.
That the data set has been ranked for lowest to highest.
Which percentile is desired, the 0th percentile up through the 100th percentile.

Which percentile is desired, the 0th percentile up through the 100th percentile.

The value of the third quartile (Ǫ3) can be less than the value of the first quartile (Ǫ1).

TRUE or FALSE

FALSE

How many data values are less than the value of the third quartile (Ǫ3)?

Three quarters (75%)of the data values.
One third (33%) of the data values.
One quarter (25%) of the data values.
The middle half (50%) of the data values.

Three quarters (75%)of the data values.

Percentiles (Pk) (or quartiles (Ǫk) must always be a data value in the data set.

TRUE or FALSE

FALSE

Which of the answers below are NOT one of the steps to find any percentile (Pk)?

Step 3: Find the Value of the percentile from the ranked data set.
None of the other choices.
Step 1: Calculate the Index.
Step 2: Move to the correct Position.

None of the other choices.

The appropriate equation to use in Step 1: Calculate the Index of finding a percentile (Pk)is shown below.

i=k100×n

TRUE or FALSE

TRUE

In Step 2: Move to the correct position of finding a percentile (Pk), how is the appropriate move decided?

-If i is an integer, move up to the next higher data value. If i has a decimal, average that and the next higher data values .
-If i is an integer, average that and the next lower data values. If i has a decimal, move down to the next lower data value.
-If k/100 is less than 0.5, move down to the next lower data value. If k/100 is greater than 0.5, move up to the next higher data value.
-If i is an integer, average that and the next higher data values. If i has a decimal, move up to the next higher data value.

If i is an integer, average that and the next higher data values. If i has a decimal, move up to the next higher data value.

What is the 40th percentile (P40) in the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9, 13, 14, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193

18.5

What is the first quartile (Ǫ1) / third quartile (Ǫ3) in the following ranked set of data (n = 15)? (to one decimal place = 00.0)
9,13, 14, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193

14 / 40
13.5 / 40.5
14 / 41
13 / 40

14 / 41

What is the 60th percentile (P60) in the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9, 13, 14, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193

33.5

What is the 90th percentile (P90) in the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9, 13, 14, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193

44

What is sum of the data values less than the 20th percentile (P20) the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9, 13, 14, 15, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193

36

What is the value of the median (M) in the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9, 13, 14, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193

24

What is the value of the interquartile range (IQR)in the following ranked set of data (n = 15)? (to one decimal place = 00.0)

9, 13, 14, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 193

27

The interquartile range (IQR) can never be negative.

TRUE or FALSE

TRUE

The range is a reliable measure of spread.

TRUE or FALSE

FALSE

The interquartile range (IQR) measures the spread of what part of the data set?

Middle half (50%)
Upper half (50%)
Middle third (33%)
Middle majority (90%)

Middle half (50%)

What does a larger value for the interquartile range (IQR) mean about the data values?

The values of the data values are spread wider apart.
The median is larger.
The values of the data values are spread narrower together.
There are fewer data values less than the first quartile (Ǫ1) and greater than the third quartile (Ǫ3).

The values of the data values are spread wider apart.

What information is given by a five number summary?

All of these other answers.
It gives the median as a measure of location.
It gives the min and the max as a non-resistant measure of spread.
It gives the quartiles as a resistant measure of spread

All of these other answers.

Are there any extreme values in the ranked set of data below (n = 15)?
-19, -3, 11, 14, 15 18, 19, 24, 30, 37 40, 41, 44, 44, 90

There are no extreme values in this data set because all the data values are inside the fences.
Both -19 and 90 are extreme values.
90 is an extreme value because the upper fence is 81.5.
-19 is an extreme value because the lower fence is -27.5.

90 is an extreme value because the upper fence is 81.5.

Regarding a five number summary, what are the fences used for?

To find the most appropriate min and max.
To give a lower limit and an upper limit on the data values to detect extreme values.
To provide limits in which to use efficient statistics.
To keep the data values together for analysis.

To give a lower limit and an upper limit on the data values to detect extreme values.

What is the value of the lower fence, and of the upper fence, in the five number summary below?
{0.2, 6.05, 6.45, 6.95, 8.2}

0.2, and 8.2
5.15, and 7.85
-1.15, and 9.55
4.70, and 8.30

4.70, and 8.30

Are there any extreme values in the data set that has the five number summary below?
{0.2, 6.05, 6.45, 6.95, 8.2}

A histogram of this data set does not show any extreme values.
0.2 and 8.2 are both extreme values as they are outside of the fences.
0.2 because the lower fence is 4.70.
No extreme values because the fences are -1.15 and 9.55,

0.2 because the lower fence is 4.70.

Why is the distribution of a data set so important?

Because the distribution describes the data values in the data set.
Because the distribution tells how the data values are distributed.
Because the distribution can be used to find the probability of an event.
Because distribution is an easy way to look at the shape, location, and spread of the data values.

Because the distribution can be used to find the probability of an event.

What information does an area under the normal curve give?

The event being studied.
The size of the event of interest.
The probability of an event.
The range of the probability of an event.

The probability of an event.

Why is the probability of an event so important in the science of statistics?

Probability of an event gives the likelihood of the event
Probability of an event can be used in advanced statistical methods.
Probability of an event can be used to make a bet.
Probability of an event can be used to make a better decision.

Probability of an event can be used to make a better decision.

The probability of an event can mean two things:

1. The proportion of the population described by the event.
2. The chance an individual will be randomly selected.

TRUE or FALSE

FALSE

What are the critical parameters of a normal curve?

Mean (µ) and standard deviation (σ).
x and y.
Uni-modal and symmetrical.
Bell shape and an area of 1.

Mean (µ) and standard deviation (σ).

Only one critical parameter is needed to calculate probability with a normal curve.

TRUE or FALSE

FALSE

A normal curve can be described with one specific mathematical equation, if the values of the variables are known.

TRUE or FALSE

TRUE

The curve below is a normal curve.

TRUE or FALSE

FALSE

On a real number line, a change in the mean shifts a normal curve horizontally, and a change in the standard deviation shifts the normal curve vertically.

TRUE or FALSE

FALSE

Standard deviation (σ) is another way to give the width of a normal curve

TRUE or FALSE

TRUE

If the area under a normal curve less than z = -1.75 equals 0.04, what is the area under the curve to the right of z = -1.75?

0.96

If the area under a normal curve less than z = -1.75 equals 0.04, what is the area under the curve greater than z = +1.75?

0.04

If the area under a normal curve less than z = -1.75 equals 0.04, what is the area under the curve between z = -1.75 and z = +1.75?

0.92

For the Shapiro-Wilk test for normality, a P-value = 0.25 means that the data follow a normal shape.

TRUE or FALSE

TRUE

Which of the following answers is NOT true of a statistical event.

An event is an interval on the x-axis.
An event lies between -∞ and +∞.
An event can be a in the tail, in the body, or on the side of a normal curve.
An event is an area under a normal curve.

An event is an area under a normal curve.

What is the appropriate mathematics to use to find a left tail area?

An area from the z-table - 1 .
An area from the z-table - an area from the z-table.
An area from the z-table.
1 - an area from the z-table.

An area from the z-table.

What is the appropriate mathematics to use to find a two-tail area?

An area from the z-table + an area from the z-table.
An area from the z-table / an area from the z-table .
An area from the z-table - an area from the z-table.
(An area from the z-table) * 2

An area from the z-table + an area from the z-table.

What is the appropriate mathematics to use to find a right body area?

An area from the z-table - an area from the z-table.
An area from the z-table.
1 - An area from the z-table.
An area from the z-table - 1.

1 - An area from the z-table.

What is the appropriate mathematics to use to find a middle body area?

A left area from the z-table - a right area from the z-table.
A left area from the z-table + a right area from the z-table - 1.
1 - a left area from the z-table - a right area from the z-table.
A left area and a right area from the z-table.

1 - a left area from the z-table - a right area from the z-table.

What is the appropriate mathematics to use to find a right-side area?

A left area from the z-table + a right area from the z-table - 1.
The larger area from the z-table + the smaller area from the z-table.
1 - the larger area from the z-table.
The larger area from the z-table - the smaller area from the z-table.

The larger area from the z-table - the smaller area from the z-table.

The areas defined in the Empirical Rule of statistics are valid for all normal curves.

TRUE or FALSE

TRUE

What is the area under a normal curve between the mean plus one standard deviation (µ+1σ), and the mean plus two standard deviations (µ+2σ)?

13.5