Quiz about Histogram Quiz

Question 1

What is a histogram primarily used for?

Accepted Answer

Displaying the shape of a distribution for a large number of observations

Answer

Comparing two categorical variables

Answer

Showing the relationship between two variables

Answer

Representing data in a pie chart

Question 2

What type of variable is a histogram most useful for displaying?

Accepted Answer

Quantitative variable

Answer

Categorical variable

Answer

Nominal variable

Answer

Ordinal variable

Question 3

What does a histogram plot on the vertical axis?

Accepted Answer

The counts of data values in each class

Answer

The mean of the data values

Answer

The sum of all data values

Answer

The range of data values

Question 4

What is the purpose of relative frequencies in some histograms?

Accepted Answer

To represent the proportion of data in each class

Answer

To show the total number of observations

Answer

To calculate the mean of the data

Answer

To display the range of the data

Question 5

What is the primary purpose of interpreting histograms?

Accepted Answer

To understand the shape, center, spread, and outliers in a dataset

Answer

To create visually appealing graphs

Answer

To compare different datasets visually

Answer

To calculate the mean and median of a dataset

Question 6

What does the 'center' in a histogram represent?

Accepted Answer

The approximate location where the distribution is balanced

Answer

The highest frequency in the dataset

Answer

The total number of observations in the dataset

Answer

The range of possible values in the dataset

Question 7

What does 'spread/variability' in a histogram indicate?

Accepted Answer

The range and how spread out the values are

Answer

The total number of observations

Answer

The shape of the distribution

Answer

The center of the distribution

Question 8

What type of information does the 'shape' of a histogram provide?

Accepted Answer

The overall pattern of the distribution

Answer

The number of observations in the dataset

Answer

The type of variable being measured

Answer

The range of possible values

Question 9

What is an outlier in a data distribution?

Accepted Answer

An individual observation that falls outside the overall pattern of the distribution.

Answer

An observation that falls within the overall pattern of the distribution.

Answer

A value that is always naturally occurring.

Answer

A measurement error that aligns with the distribution.

Question 10

What should you do when you encounter an outlier in a dataset?

Accepted Answer

Investigate the observation further.

Answer

Ignore it and proceed with the analysis.

Answer

Assume it is a naturally occurring value.

Answer

Remove it immediately from the dataset.

Question 11

What does a symmetric histogram indicate?

Accepted Answer

The left and right sides of the histogram are approximately mirror images.

Answer

The right side of the histogram extends much farther out than the left side.

Answer

The left side of the histogram extends much farther out than the right side.

Answer

The histogram shows two separate peaks.

Question 12

What is a histogram called if the right side extends much farther out than the left side?

Accepted Answer

Skewed right histogram.

Answer

Symmetric histogram.

Answer

Skewed left histogram.

Answer

Multimodal histogram.

Question 13

Which type of histogram shows one dominant peak?

Accepted Answer

Unimodal histogram.

Answer

Bimodal histogram.

Answer

Multimodal histogram.

Answer

Skewed histogram.

Question 14

What is a bimodal histogram?

Accepted Answer

A histogram with two separate peaks.

Answer

A histogram with all bars roughly the same height.

Answer

A histogram with one dominant peak.

Answer

A histogram with a long right tail.

Question 15

What does a multimodal histogram represent?

Accepted Answer

A histogram where all bars are roughly the same height.

Answer

A histogram with one dominant peak.

Answer

A histogram with two separate peaks.

Answer

A histogram with a long left tail.

Question 16

What does a stem-and-leaf plot help to organize and display?

Accepted Answer

Quantitative data while preserving actual data values.

Answer

Qualitative data without preserving actual data values.

Answer

Only the frequency of data points.

Answer

Only the average of data points.

Question 17

In a stem-and-leaf plot, what does the 'stem' represent?

Accepted Answer

The leading digit(s) of each number.

Answer

The trailing digit(s) of each number.

Answer

The average of all digits in the number.

Answer

The sum of all digits in the number.

Question 18

In a stem-and-leaf plot, what does the 'leaf' represent?

Accepted Answer

The trailing digit(s) of each number.

Answer

The leading digit(s) of each number.

Answer

The sum of all digits in the number.

Answer

The frequency of the number.

Question 19

How should the stems be arranged in a stem-and-leaf plot?

Accepted Answer

Vertically with the smallest at the top.

Answer

Horizontally with the largest at the left.

Answer

Horizontally with the smallest at the left.

Answer

Vertically with the largest at the top.

Question 20

How should the leaves be arranged in a stem-and-leaf plot?

Accepted Answer

In a row to the right of the stem, in increasing order.

Answer

In a row to the left of the stem, in decreasing order.

Answer

In a column below the stem, in random order.

Answer

In a column above the stem, in increasing order.

Question 21

What is the percentile for a number with 60% of the data above it?

Accepted Answer

40th percentile

Answer

60th percentile

Answer

50th percentile

Answer

30th percentile

Question 22

What is the standard score for a woman whose length of pregnancy is 236 days, given a mean of 266 days and a standard deviation of 16 days? (Round answer to two decimal places.)

Accepted Answer

-1.88

Answer

-2.00

Answer

-1.50

Answer

-1.75

Question 23

The diagram shows percentiles, including the lowest 1%, 2%, 3%, and highest 1%, 2%, 3%. Which of the following best describes what the lowest 1% represents?

Accepted Answer

The bottom 1% of values in the data set

Answer

The top 1% of values in the data set

Answer

The middle 1% of values in the data set

Answer

The average value of the data set

Question 24

According to Chebyshev's Inequality, what percentage of the data will be within two standard deviations of the mean?

Accepted Answer

75%

Answer

50%

Answer

88.9%

Answer

95%

Question 25

According to Chebyshev's Inequality, what percentage of the data will be within three standard deviations of the mean?

Accepted Answer

88.9%

Answer

75%

Answer

95%

Answer

99%

Question 26

If the mean score of a group of students is 75 and the standard deviation is 8, what is the range of scores within which at least 75% of the students scored?

Accepted Answer

Between 59 and 91

Answer

Between 67 and 83

Answer

Between 50 and 100

Answer

Between 70 and 80

Question 27

If the mean score of a group of students is 75 and the standard deviation is 8, what is the range of scores within which at least 88.9% of the students scored?

Accepted Answer

Between 51 and 99

Answer

Between 67 and 83

Answer

Between 59 and 91

Answer

Between 70 and 80

Question 28

What does the area under the normal curve over an interval represent in statistics?

Accepted Answer

The proportion of the population contained within the interval.

Answer

The total number of observations in the population.

Answer

The mean of the population.

Answer

The standard deviation of the population.

Question 29

What is the formula for calculating the standard score (z-score)?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Answer

$$z = \frac{\sigma - x}{\mu}$$

Answer

$$z = \frac{\mu - x}{\sigma}$$

Answer

$$z = \frac{x + \mu}{\sigma}$$

Question 30

What does a positive z-score indicate about an observation $ x $?

Accepted Answer

The observation is above the mean.

Answer

The observation is below the mean.

Answer

The observation is equal to the mean.

Answer

The observation is unrelated to the mean.

Question 31

What does a negative z-score indicate about an observation $ x $?

Accepted Answer

The observation is below the mean.

Answer

The observation is above the mean.

Answer

The observation is equal to the mean.

Answer

The observation is unrelated to the mean.

Question 32

Why are standard scores (z-scores) considered unitless?

Accepted Answer

Because they are used to compare observations from different populations.

Answer

Because they are expressed in terms of percentages.

Answer

Because they are always equal to zero.

Answer

Because they are measured in standard deviation units.

Question 33

What does a z-score of 1 indicate about the woman's height in the example provided?

Accepted Answer

Her height is one standard deviation above the mean height.

Answer

Her height is one standard deviation below the mean height.

Answer

Her height is equal to the mean height.

Answer

Her height is unrelated to the mean height.

Question 34

What are the mean and standard deviation of the standard normal distribution?

Accepted Answer

Mean = 0, Standard deviation = 1

Answer

Mean = 1, Standard deviation = 0

Answer

Mean = 0, Standard deviation = 0

Answer

Mean = 1, Standard deviation = 1

Question 35

What is the 25th percentile of a distribution also known as?

Accepted Answer

The first quartile (Q1)

Answer

The median

Answer

The third quartile (Q3)

Answer

The mean

Question 36

What is the 75th percentile of a distribution also known as?

Accepted Answer

The third quartile (Q3)

Answer

The median

Answer

The first quartile (Q1)

Answer

The mean

Question 37

What does the pth percentile of a distribution represent?

Accepted Answer

A value such that p percent of the observations lie below it and the rest above

Answer

A value such that p percent of the observations lie above it and the rest below

Answer

A value such that p percent of the observations lie equally above and below it

Answer

A value such that p percent of the observations lie randomly distributed

Question 38

What does a z-score of -0.33 indicate about the woman's height?

Accepted Answer

Her height is 0.33 standard deviations below the mean height.

Answer

Her height is 0.33 standard deviations above the mean height.

Answer

Her height is equal to the mean height.

Answer

Her height is 1 standard deviation below the mean height.

Question 39

Suppose SAT Math scores are normally distributed with a mean of 500 and a standard deviation of 100. What is Sarah's z-score if she scored 550 on the SAT Math exam?

Accepted Answer

0.5

Answer

-0.5

Answer

1.0

Answer

-1.0

Question 40

Suppose ACT Math scores are normally distributed with a mean of 18 and a standard deviation of 6. What is Bill's z-score if he scored 15 on the ACT Math exam?

Accepted Answer

-0.5

Answer

0.5

Answer

-1.0

Answer

1.0

Question 41

Suppose ACT Math scores are normally distributed with a mean of 18 and a standard deviation of 6. What is Julie's z-score if she scored 24 on the ACT Math exam?

Accepted Answer

1.0

Answer

-1.0

Answer

0.5

Answer

-0.5

Question 42

Who performed best among Bill, Sarah, and Julie relative to their own testing group based on z-scores?

Accepted Answer

Julie

Answer

Sarah

Answer

Bill

Answer

All performed equally well

Question 43

What is a population represented by a normal curve said to be?

Accepted Answer

Normally distributed

Answer

Randomly distributed

Answer

Uniformly distributed

Answer

Exponentially distributed

Question 44

Which of the following is a property of normal distributions?

Accepted Answer

Normal distributions are symmetric around the mode

Answer

Normal distributions have multiple modes

Answer

The mean, median, and mode of a normal distribution are all different

Answer

Normal distributions are skewed

Question 45

What determines the center of a normal distribution?

Accepted Answer

The mean

Answer

The standard deviation

Answer

The mode

Answer

The inflection point

Question 46

What does the standard deviation determine in a normal curve?

Accepted Answer

The variability of the curve

Answer

The center of the curve

Answer

The symmetry of the curve

Answer

The inflection point

Question 47

What is the inflection point in a normal curve?

Accepted Answer

The point where the curve changes from "opening down" to "opening up"

Answer

The center of the curve

Answer

The mean of the curve

Answer

The standard deviation of the curve

Question 48

What happens to the shape of a Normal distribution when the mean is changed?

Accepted Answer

The shape does not change, only its location on the axis changes.

Answer

The shape becomes narrower.

Answer

The shape becomes wider.

Answer

The shape becomes skewed.

Question 49

What happens to the shape of a Normal distribution when the standard deviation is changed?

Accepted Answer

The shape becomes narrower or wider depending on the change in standard deviation.

Answer

The shape does not change, only its location on the axis changes.

Answer

The shape becomes skewed.

Answer

The shape becomes flat.

Question 50

What is the 68-95-99.7 rule also known as?

Accepted Answer

The empirical rule.

Answer

The standard deviation rule.

Answer

The probability rule.

Answer

The Gaussian rule.

Question 51

According to the 68-95-99.7 rule, approximately what percentage of observations fall within one standard deviation of the mean in a Normal distribution?

Accepted Answer

68%

Answer

95%

Answer

99.7%

Answer

50%

Question 52

According to the 68-95-99.7 rule, approximately what percentage of observations fall within two standard deviations of the mean in a Normal distribution?

Accepted Answer

95%

Answer

68%

Answer

99.7%

Answer

75%

Question 53

According to the 68-95-99.7 rule, approximately what percentage of observations fall within three standard deviations of the mean in a Normal distribution?

Accepted Answer

99.7%

Answer

68%

Answer

95%

Answer

100%

Question 54

What does the empirical rule help estimate in a Normal distribution?

Accepted Answer

The probabilities for data without complex calculations.

Answer

The mean of the data set.

Answer

The skewness of the data set.

Answer

The mode of the data set.

Question 55

What is the characteristic of a symmetric density curve?

Accepted Answer

The left and right sides of the density curve are mirror images.

Answer

The right side of the density curve extends farther out than the left side.

Answer

The left side of the density curve extends farther out than the right side.

Answer

The density curve has two separated peaks.

Question 56

What does it mean when a density curve is skewed right?

Accepted Answer

The right side of the density curve extends farther out than the left side.

Answer

The left side of the density curve extends farther out than the right side.

Answer

The density curve has two separated peaks.

Answer

The density curve has only one prominent peak.

Question 57

What is the term used to describe a density curve with only one prominent peak?

Accepted Answer

Unimodal

Answer

Symmetric

Answer

Bimodal

Answer

Skewed

Question 58

What is the median of a density curve?

Accepted Answer

The value with half the area to the left and half the area to the right.

Answer

The balancing point of the density curve.

Answer

The value with 0.25 area under the curve to the left of it.

Answer

The value with 0.75 area under the curve to the left of it.

Question 59

What is the mean of a density curve?

Accepted Answer

The balancing point of the density curve.

Answer

The value with half the area to the left and half the area to the right.

Answer

The value with 0.25 area under the curve to the left of it.

Answer

The value with 0.75 area under the curve to the left of it.

Question 60

For a symmetric density curve, what is the relationship between the mean and the median?

Accepted Answer

The mean and the median are the same, located at the center.

Answer

The mean is farther out in the long tail than the median.

Answer

The mean is closer to the left side than the median.

Answer

The mean is closer to the right side than the median.

Question 61

For a skewed density curve, where is the mean located in relation to the median?

Accepted Answer

The mean is farther out in the long tail than the median.

Answer

The mean and the median are the same, located at the center.

Answer

The mean is closer to the left side than the median.

Answer

The mean is closer to the right side than the median.

Question 62

What does a bimodal density curve indicate?

Accepted Answer

The density curve has two separated peaks.

Answer

The density curve has only one prominent peak.

Answer

The left side of the density curve extends farther out than the right side.

Answer

The right side of the density curve extends farther out than the left side.

Question 63

What is a density curve?

Accepted Answer

A smoothed-out, idealized version of a histogram.

Answer

A graphical representation of raw data points.

Answer

A chart showing the frequency of data points.

Answer

A scatter plot of population distribution.

Question 64

What does a density curve represent?

Accepted Answer

The proportion of observations in any region.

Answer

The total number of data points in a dataset.

Answer

The average value of a dataset.

Answer

The maximum and minimum values of a dataset.

Histogram Quiz

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