Font size
WorksheetsPage 1
Total questions: 150
Worksheet time: 1hrs 15mins
Which measure of central tendency is the value that occurs most frequently in a data set?
Median separating two halves
Mode appearing most often
Mean of all observations
Midrange average of extremes
For the data set 5, 7, 7, 9, 12, what is the median?
Eight point zero
Seven point eight
Nine point zero
Seven point zero
Which statement best describes the mean of a data set?
Middle position after ordering
Sum divided by count
Most repeated value
Difference of highest and lowest
A teacher records quiz scores: 10, 8, 7, 10, 6. What is the mode of the scores?
Eight only
Ten only
Six only
Seven only
Which measure is most affected by an extreme outlier in the data?
Mode of the data
Median of the data
Mean of the data
Range of categories
The range of a data set is defined as which computation?
Sum divided by count
Highest plus lowest
Lowest divided by count
Highest minus lowest
A data set has values: 4, 6, 8, 10. What is the mean?
Seven point zero
Seven point five
Eight point five
Eight point zero
Which graphical display is best for showing the distribution of numerical data across intervals?
Bar chart of categories
Histogram with bins
Pie chart of shares
Line graph of trends
A sample of 9 students’ heights is taken to estimate average height of the class. This is an example of which concept?
Descriptive listing
Parameter estimation
Random sampling
Population census
A dataset is skewed right with one very large value. Which measure best represents its center?
Midrange of extremes
Mean of the data
Median of the data
Mode of the data
Which of the following is a nominal level of measurement?
Gender
Weight
Height
Temperature
Which level of measurement arranges data by rank but not equal intervals?
Nominal categories without order
Ordinal ranks without equal gaps
Interval values with true zero
Ratio measures with absolute zero
Which of the following is an example of an ordinal level of measurement?
Rating on a satisfaction scale
Temperature in degrees Celsius
Income in dollars per month
Age measured in years
Which measure is appropriate for nominal data like hair color?
Mode of the categories
Standard deviation of colors
Median of the labels
Mean of the categories
A Likert-scale response (Strongly disagree to Strongly agree) is best treated as which type?
Interval equal-interval scale
Ratio scale with true zero
Nominal unordered labels
Ordinal ordered categories
Which statement correctly distinguishes interval from ratio scales?
Both have true zero reference
Interval lacks true zero; ratio has it
Neither allows meaningful differences
Interval has true zero; ratio lacks it
Choose the best summary measure for ordinal data with skewed ranks.
Variance of the ranks
Median of the ordered data
Mean of rank numbers
Geometric mean of ranks
If temperatures in °C are converted to °F, which property is preserved?
Ratio comparisons like twice as hot
Counts of observations
Order of the measurements
Absolute zero value
Which dataset is most appropriate for a bar chart rather than a histogram?
Favorite sports categories
Test scores from 0 to 100
Heights of students in centimeters
Daily rainfall amounts
A survey asks students to rank four lunch options from 1 to 4. What analysis is most suitable?
Compute the mean rank value
Report the median rank per option
Compare ratios of ranks
Perform linear regression on ranks
Which measurement level allows meaningful addition and subtraction but not ratio statements like “twice as much”?
Ratio scale values
Ordinal ranking only
Nominal classification only
Interval scale values
Which of the following is an example of an interval level of measurement?
Fahrenheit temperature
Number of siblings
Social security number
Year of birth
Which of the following is an example of a ratio level of measurement?
Favorite color
Height
IQ score
Zip code
Which level of measurement has a true zero, allowing meaningful ratios like "twice as much"?
Interval
Ordinal
Ratio
Nominal
Which variable type categorizes data without any inherent order?
Nominal
Ordinal
Interval
Ratio
Which measure is most appropriate for central tendency of nominal data?
Midrange
Mode
Median
Mean
A Celsius temperature of 20 and 10 cannot form a ratio like "twice as hot" because Celsius lacks a true zero. What level of measurement is Celsius temperature?
Nominal
Ordinal
Ratio
Interval
Student test ranks (1st, 2nd, 3rd) represent which level of measurement?
Nominal
Ordinal
Ratio
Interval
Which statement is correct about ratio data?
Has categories with no order
Has equal intervals without true zero
Has equal intervals and true zero
Has order but unequal gaps
ZIP codes best illustrate which level of measurement?
Ratio
Ordinal
Interval
Nominal
Which example fits interval level of measurement?
Birth year differences in decades
Number of books owned
Ranking movies from best to worst
Types of fruit preferred
Why is "favorite color" not ratio level?
Meaningful ratios possible
Has order but not equal gaps
Intervals equal but no zero
No numeric scale or true zero
Which level of measurement is most commonly used in surveys?
Interval
Ordinal
Nominal
Ratio
Which level of measurement classifies data into mutually exclusive categories without order?
Interval scale equal differences
Ratio scale true zero values
Ordinal scale ranked categories
Nominal scale categories only
Which level of measurement provides ranked order but not equal intervals between ranks?
Interval level equal spacing
Nominal level categories only
Ratio level meaningful zeros
Ordinal level rankings only
Which level of measurement has equal intervals but lacks a true zero point?
Interval scale equal differences
Ratio scale absolute zero
Ordinal scale ordered ranks
Nominal scale unordered labels
Which level of measurement allows for all arithmetic operations because it includes a true zero?
Interval scale without zero
Ratio scale with true zero
Nominal scale category labels
Ordinal scale ranked order
A survey records eye color as brown, blue, or green. What measurement level is used?
Nominal categories only
Ordinal ranked levels
Interval equal spacing
Ratio true zero point
Race placement in a marathon (1st, 2nd, 3rd) represents which measurement level?
Ordinal ranked positions
Nominal category labels
Ratio absolute zero
Interval equal differences
Temperature measured in Celsius is best classified at which level?
Ratio true zero value
Ordinal ordered ranks
Nominal simple categories
Interval no true zero
Weight measured in kilograms is at which level of measurement?
Interval scale no zero
Ordinal scale ranking
Nominal scale labeling
Ratio scale true zero
Which statement correctly distinguishes interval from ratio scales?
Interval lacks true zero
Ratio lacks equal spacing
Ratio provides only rankings
Interval provides unordered labels
Which operation is valid for ratio data but not for interval data?
Simple addition only
Categorizing by names
Ranking without numbers
Meaningful multiplication
Which measure of central tendency summarizes data by averaging all values?
Range between extremes
Mode of repeated values
Median of ordered values
Mean of the dataset values
Which measure is least affected by extreme outliers in a skewed dataset?
Mean across all values
Median at middle position
Range from min to max
Mode as most frequent
In a dataset, the mode represents which feature?
Average of all numbers
Difference between highest and lowest
Middle value when ordered
Most frequently occurring value
Which statement correctly defines the range of a dataset?
Count of distinct categories
Sum of all data points
Average minus the median
Highest value minus lowest value
A teacher records quiz scores: 6, 7, 7, 8, 9. What is the mean score?
7.4 after averaging
7.0 as middle value
7.0 as most frequent
3.0 as score spread
For the scores 2, 3, 3, 9, 12, which measure best represents central tendency?
Range summarizing center
Mean due to symmetry
Median robust to outliers
Mode describing typical score
A dataset has two equally common values. What is this situation called?
Bimodal distribution
Unimodal dataset
Trimodal dataset
Uniform distribution
Which change will increase the mean but leave the median unchanged?
Shift all values equally
Duplicate the middle value
Remove the lowest value
Add a large outlier
Test scores: 50, 60, 60, 70, 100. Which measure is most influenced by 100?
Mode as common score
Median as middle score
Range as score spread
Mean across all scores
Which measure is most appropriate for categorical data like favorite fruit?
Mode of categories
Median across categories
Mean of categories
Range between categories
Which measure of central tendency is least affected by extreme values in a dataset?
Median of ordered data
Mean of all observations
Mode of most frequent value
Range between max and min
A dataset of 9 exam scores is skewed by one very low score. Which measure best represents the typical performance?
Range of highest minus lowest
Mode of repeated score
Median of ordered scores
Arithmetic mean of scores
Which statement correctly describes the median for an even-sized dataset?
It equals the most frequent value
It is the largest minus smallest
It is the middle value after sorting
It is the average of the two middles
For the data 4, 4, 5, 6, 100, which measure changes the most if 100 is replaced by 10?
Median of the data
Mode of the data
Mean of the data
Range of the data
A teacher wants a measure that summarizes the center and is resistant to outliers. Which should be chosen?
Sample mean of scores
Sample median of scores
Sample mode of scores
Score range measure
Which measure requires data to be at least ordinal (able to be ordered)?
Mode of categories
Range of unordered items
Mean of coded labels
Median of ordered values
In a right-skewed distribution, which inequality most often holds among mean, median, mode?
Mean < Median < Mode
Mean = Median = Mode
Mode < Median < Mean
Median < Mode < Mean
You compute the mean height as 160 cm, but two extreme values were data entry errors. What is the best immediate action?
Verify entries then recompute mean
Remove errors then recompute median
Report mean without changes
Apply range to replace the mean
Which dataset property does the range primarily measure?
Central location of data
Symmetry around the center
Frequency of typical value
Overall spread of values
A set of salaries includes an outlier CEO salary. Which measure best reflects typical employee pay?
Company-wide range salary
Company-wide mean salary
Company-wide median salary
Company-wide mode salary
What is the median?
The value that occurs most frequently in a data set
The value that is closest to the arithmetic mean in a data set
The middle value in a data set
The value halfway between minimum and maximum values in a data set
What is the mode?
The middle value when data are ordered
The value closest to the arithmetic mean
The value occurring most frequently in a dataset
The value halfway between minimum and maximum
Which measure identifies the center of an ordered dataset?
Mode identifies the most common value
Median identifies the central value
Range identifies the spread endpoints
Variance identifies average squared deviations
A dataset is 3, 4, 4, 5, 6. What is the mode?
6
4
3
5
In 10, 12, 12, 14, 16, which measure equals 12?
Range equals 12 from min to max
Mode equals 12 as most frequent
Median equals 12 after ordering
Mean equals 12 over all values
Which statement about mode is true?
Mode requires ordered data to compute
Mode must be unique in any dataset
Mode always equals the mean
A dataset can have multiple modes
Which dataset has no mode?
7, 8, 8, 9, 10
2, 3, 4, 5, 6
5, 5, 6, 7, 8
1, 2, 2, 3, 3
You need the most popular shoe size in a class. Which measure should you use?
Mean because it uses all values
Median because it is robust
Mode because it is most frequent
Range because it shows spread
Which change can alter the mean but not the mode?
Sorting the dataset differently
Duplicating the most common value
Removing the most common value
Adding a new unique extreme value
For 2, 2, 3, 3, 4, what are the modes?
Only 2
Only 3
2 and 3
2 and 4
Which best explains why mode is useful for categorical data?
It averages labels mathematically
It identifies the most common category
It orders categories by magnitude
It measures variability among categories
What is the range?
The middle value in a dataset
The value that occurs most frequently in a dataset
The average of the highest and lowest values in a dataset
The difference between the highest and lowest values in a dataset
What is the difference between the sample mean and the population mean?
The sample mean estimates the population mean
The population mean is always higher
The sample mean is always higher
There is no difference between them
What is the standard deviation?
A measure of the average distance of each value from the mean.
The difference between the highest and lowest values in a dataset.
The average of the highest and lowest values in a dataset.
The number of standard errors the sample mean is from the population mean.
Find the mean of the dataset: 10, 20, 30, 40, 50
20
30
35
40
Which measure of central tendency is most affected by extreme values in a dataset?
Median
Mean
Mode
Midrange
For the data 3, 7, 7, 9, 12, what is the median?
7
8
9
10
A dataset has values 5, 5, 6, 7, 7, 7, 9. What is the mode?
5
9
6
7
The range of a dataset is defined as which expression?
Median minus mode
Sum divided by count
Mean minus median
Maximum minus minimum
Compute the range for data: 2, 4, 6, 9, 15
7
11
13
9
Which statement is true about median in a skewed distribution?
More affected by extremes
Less affected by outliers
Always equals the mean
Always equals the mode
The mean of five numbers is 12. If four of them are 10, 11, 12, 13, what is the fifth number?
12
13
15
14
In a frequency table, what does relative frequency represent?
Product of counts
Proportion of total
Sum of values
Difference of extremes
You add 5 to every value in a dataset. Which measure changes by 5?
Mean only
Median only
Mode only
Mean and median
Find the median of the following dataset: 2, 4, 6, 8, 10, 12
4
6
8
10
What is a random variable?
A variable that has a fixed value
A variable whose value depends on a random event
A variable not determined by chance
A variable that only takes discrete values
Which statement best describes a discrete random variable?
It can take any real number value
It takes countable separate values
It is not affected by probability
It always follows a normal curve
Which example is a discrete random variable?
The exact height of students
The number of heads in ten flips
The mass recorded to decimals
The temperature measured continuously
Which example is a continuous random variable?
Number of red marbles drawn
Time taken to finish a race
Count of cars passing a point
Number of books on a shelf
What does the probability distribution of a random variable show?
All possible outcomes only
Outcomes with assigned probabilities
Only the most likely outcome
A list of unrelated values
For a fair six-sided die, what is P(X=4) if X is the outcome?
1/2
1/3
1/6
0
A variable Y equals the number of goals in a match. Which type is Y?
Non-random value
Discrete random variable
Continuous random variable
Deterministic function
Which statement is true about continuous variables?
They cannot be measured
They are always integer counts
They take infinitely many values
They have gaps between values
If Z is the time a bus arrives, why is Z random?
It is independent of traffic
It only takes integer minutes
It depends on chance factors
It has a fixed schedule always
Which option correctly contrasts discrete and continuous variables?
Discrete are counts; continuous measured
Discrete follow normal; continuous are uniform
Discrete are measured; continuous counted
Discrete have decimals; continuous are integers
Which statement best defines the expected value of a random variable?
The minimum possible outcome the variable allows
The maximum possible outcome the variable allows
The average value over many identical trials
The mode the random variable most often shows
A fair six-sided die is rolled once. What is the expected value of the outcome?
Three point five as the long-run average
Three because it is near the middle
Four because higher numbers are likely
Six because it is the maximum value
Which measure is most affected by extreme outliers in a dataset?
The mean because it uses all values
The range because it uses endpoints
The median because it uses positions
The mode because it uses frequency
In a dataset of test scores, which measure best represents the typical score when outliers exist?
Mean because it averages all scores
Range because it shows spread
Median because it resists outliers
Mode because it is most common
A distribution is symmetric and unimodal. Which statement is true about mean and median?
Mean and median are unrelated in symmetric unimodal
Median exceeds mean in symmetric unimodal
Mean exceeds median in symmetric unimodal
Mean equals median in symmetric unimodal
A class records the number of books read per student: 2, 3, 2, 4, 2, 5. What is the mode?
Five because it is the largest value
Four because it is the average value
Three because it is near the center
Two because it appears most often
The range of a dataset equals 18 and the minimum value equals 7. What is the maximum value?
Seven using range minus min
Twenty-five using max minus min
Eleven using range plus min
Thirty using min plus twice range
Which action would decrease the variance of a dataset?
Values cluster closer to the mean
Values move farther from the mean
Outliers appear at both extremes
The mean shifts without dispersion
A probability distribution has outcomes 0 and 10 with probabilities 0.9 and 0.1. What is the expected value?
Five because it is the middle value
Zero because 0 dominates probability
One because 0.9×0 + 0.1×10
Ten because it is the largest outcome
When adding a constant c to every data point, which measure increases exactly by c?
Mode because frequencies always change
Standard deviation because it shifts
Variance because it scales directly
Mean because it shifts uniformly
What is the variance of a random variable?
A measure of how spread out the values of the random variable are from the expected value
The highest possible value the random variable can take on
The lowest possible value the random variable can take on
The value that the random variable is most likely to take on
Which of the following is an example of a discrete variable?
The temperature outside
The height of a person
The weight of a person
The number of cars in a parking lot
Which measure describes the center of a data set by averaging all values?
Mean of the data
Interquartile range
Mode of the data
Range of the data
Which statement best distinguishes qualitative from quantitative data?
Qualitative counts measurable amounts
Quantitative uses categories or labels
Qualitative uses categories or labels
Quantitative cannot be measured numerically
Which variable type can take any value within an interval?
Discrete variable
Continuous variable
Categorical variable
Binary variable
A class survey records shoe sizes as 6, 7, 7, 8, 9. What is the mode?
Six
Nine
Eight
Seven
A data set has values 5, 7, 9, 10. What is the mean?
Eight
Seven
Seven point two five
Seven and a half
Which scenario represents a continuous measurement?
Listing jersey numbers of players
Tallying students in class
Recording daily rainfall in mm
Counting books on a shelf
A histogram shows most values clustered at lower numbers. Which measure is most affected by extreme high values?
Sample size of the data
Mean of the distribution
Mode of the distribution
Median of the distribution
You sample 30 students’ commute times to estimate schoolwide average. This is an example of which idea?
Census of all students
Sample statistic
Non-numeric category
Population parameter
Which measure summarizes spread by subtracting smallest from largest value?
Standard deviation
Median of the data
Upper quartile
Range of the data
Which of the following is an example of a continuous random variable?
The time it takes to complete a task
The number of students in one classroom
The number of heads in five coin flips
The number of cars in a single parking lot
Which measure of central tendency is found by adding all data values and dividing by the number of values?
Range of the dataset
Mean of the dataset
Median of the dataset
Mode of the dataset
A dataset has values 4, 6, 7, 7, 9. What is the median?
Seven point six
Seven point zero
Six point four
Eight point zero
Which statement best distinguishes discrete from continuous variables?
Both are counts of whole-number outcomes
Both are measurements from instruments
Discrete are measurements; continuous are counts
Discrete are counts; continuous are measurements
In a sample of 20 test scores, which measure is most affected by an extreme outlier?
Mode of the scores
Interquartile range
Median of the scores
Mean of the scores
The range of a dataset is defined as:
Average minus median value
Largest minus smallest value
Middle value after ordering
Sum divided by count value
A teacher records the heights of students to the nearest millimeter. Which variable type fits best?
Nominal categorical variable
Binary categorical variable
Continuous random variable
Discrete random variable
Which scenario would most likely produce a symmetric distribution?
Time between rare power outages
Daily rainfall in desert town
Number of pets per household
Human heights within one grade
A dataset is right-skewed. Which measure best represents its center?
Midrange of the values
Mean of the values
Mode of the values
Median of the values
Which choice correctly pairs a variable with discrete or continuous?
Mass measured on a scale — discrete
Time to run one kilometer — discrete
Age in completed years — continuous
Number of books on a shelf — discrete
What is a probability distribution?
A collection of all possible values of a variable
A set of probabilities assigned to each experiment outcome
A function describing probabilities for each random variable value
A list of equally likely outcomes for an experiment
Which statement best distinguishes a random variable from an outcome?
An outcome is a numeric summary of data
An outcome summarizes a distribution of values
A random variable maps outcomes to numbers
A random variable lists all experimental outcomes
Which option describes the sample space of an experiment?
All events that have nonzero probability
All values a random variable can take
All possible outcomes the experiment can produce
All probabilities assigned to outcomes
For a discrete random variable, which statement is true?
It has a continuous range of values
Its probabilities are given by a density
Its outcomes cannot be listed
It takes countable distinct values
Which condition must any probability distribution satisfy?
The largest probability equals one
The average probability equals zero
All probabilities are identical values
The sum of all probabilities equals one
Which choice illustrates a probability mass function (pmf)?
A boxplot summarizing data spread and center
A histogram of observed sample frequencies
A curve showing area under the function equals one
A table giving probabilities for each integer value
Suppose X is the number of heads in two coin flips. Which distribution fits X?
Uniform over {0,1,2} with equal probabilities
Binomial with n=2 and p=0.5
Poisson with rate equal to two
Normal with mean one and variance one
A function f(x) satisfies f(x) ≥ 0 and ∑ f(x) = 1 over support. What does f represent?
A cumulative distribution function
A probability mass function
A likelihood function
A probability density function
Which statement explains why option b is not the full definition of a distribution?
It ignores outcomes and only lists numbers
It depends on sample data rather than models
It omits the random variable context and mapping
It requires continuous variables exclusively
If P(X=2)=0.3, P(X=3)=0.5, and P(X=4)=0.2, what is P(X≥3)?
0.7 because probabilities must average to one
0.5 because only the largest value counts
0.5 because events share equal likelihoods
0.7 because add probabilities for 3 and 4
Which of the following is the formula for the mean (expected value) of a discrete probability distribution?
μ = ΣxP(x)
μ = ΣP(x)
μ = Σx
μ=Σ(x−μ)2P(x)
Which symbol typically represents the mean of a population in statistics?
Uppercase X
Lowercase p
Greek letter σ
Greek letter μ
In a discrete distribution, what does P(x) represent?
Mean of the data set
Cumulative distribution value
Total number of trials
Probability of outcome x
Which expression represents the variance of a discrete random variable?
ΣP(x)
Σ(x − μ)P(x)
ΣxP(x)
Σ(x−μ)2P(x)
If a random variable X takes values 1, 2, 3 with probabilities 0.2, 0.5, 0.3, what is μ?
2.1
1.9
2.0
2.3
For a valid discrete probability distribution, which condition must hold?
Σ(x−μ)2P(x)=1
ΣxP(x) = 1
Σx = 1
ΣP(x) = 1
Which step is essential when computing μ = ΣxP(x)?
Multiply each value by its probability
Subtract μ from each value first
Square each value then sum
Add probabilities without weighting
A distribution has μ = 5. Which option best describes μ?
Median of the sample
Most frequent single value
Largest possible value
Long-run average of X
Which misconception leads to an incorrect mean for discrete distributions?
Averaging x values without probabilities
Summing probabilities to find μ
Using variance formula for μ
Assuming ΣP(x) can exceed 1
You are given x values and P(x). Which formula estimates spread around μ?
μ = Σx
ΣP(x)
ΣxP(x)
Σ(x−μ)2P(x)
Which of the following is the formula for the variance of a discrete probability distribution?
σ2=Σ(x−μ)
σ2=Σ(x−μ)2P(x)
σ2=ΣP(x)
σ2=ΣxP(x)
