Statistics and Probability

Which of the following is secondary data?

In a probability scale from $0$ to $1$, where would 'an even chance' be located?

What is the mode of this data set: $2, 8, 3, 8, 2, 8, 4$?

A survey of 'Eye Color' resulted in: Brown ($12$), Blue ($5$), Green ($3$). What is the total number of people surveyed?

A relative frequency bar chart shows that the category 'Blue' has a relative frequency of $0.35$. If the total number of items surveyed was $260$, how many items were 'Blue'?

A two-digit number is chosen at random from $10$ to $99$. What is the probability that the sum of its digits is $5$?

What is the range of a data set consisting of the values: $x-3, x+2, x+8, x-5$?

A biased coin is such that the probability of heads is $0.6$. If the coin is tossed $3$ times, what is the probability of getting at least one head and at least one tail?

A sample space $S$ contains $20$ elements. Event $A$ has $8$ elements and event $B$ has $10$ elements. If $P(A \cup B) = 0.7$, how many elements are in $A \cap B$?

Three events $A, B,$ and $C$ are mutually exclusive. $P(A) = 0.2$ and $P(B) = 0.3$. What is $P(A' \cap B' \cap C')$ if $P(C) = 0.4$?

If a pie chart shows that $\frac{1}{6}$ of the students prefer Oranges, what is the central angle?

In a histogram, if the class $20-30$ has a frequency of 10 and $30-40$ has a frequency of 10, which statement is true?

A bar graph shows the number of goals scored by 4 players: A(2), B(4), C(1), D(3). What is the total number of goals?

A pie chart has a sector for 'French' that is $15\%$. How many degrees is this?

A bar graph showing favorite sports has 'Soccer' at 25 votes, 'Basketball' at 20 votes, and 'Tennis' at 5 votes. What is the central angle for 'Soccer' if this were a pie chart?

A pie chart for a 24-hour day shows 2 hours for 'Exercise'. What is the angle of this sector?

In a histogram, the class boundaries are $10, 20, 30, 40, 50$. How many class intervals are there?

In a histogram, the frequency of the class $50 \le x < 100$ is $250$. If the frequency density is plotted on a scale where $1$ unit $= 0.5$ frequency/width, what is the height of the bar in units?

A pie chart sector for 'Rent' is $120^{\circ}$. The landlord reduces the rent by $20 \%$. If all other costs remain the same, what is the percentage decrease in the angle of the 'Rent' sector?

A comparative bar graph shows that in City A, $30 \%$ of $50,000$ people recycle. In City B, $45 \%$ of $40,000$ people recycle. What is the central angle for City B's recyclers in a pie chart representing all recyclers from both cities?

Calculate the mean of the integers: $2, 4, 9$.

Find the mode of the directions: North, South, East, North, North, West.

Four students run a race. Their times are $12s, 14s, 16s, 18s$. What is the mean time?

What is the median of the following set: $12, 13, 14, 15$?

A data set is $x, x+1, x+2, x+3, x+4, x+5$. The median is $6.5$. Find the mean.

The mean of five numbers is $7$. If the numbers are in the ratio $1:2:3:4:5$, what is the largest number?

A data set: $3, 3, 5, 6, 8, 8, 8, 10, 11$. What is the sum of the mean, median, and mode? (Round mean to nearest whole number if necessary)

The mean of a set of $n$ numbers is $M$. If one number, $x$, is removed, the new mean is $M - 1$. Find $n$ in terms of $x$ and $M$.

The mean salary of $15$ employees is $\$3000$. If the manager's salary is added, the mean becomes $\$3200$. What is the manager's salary?

In a data set, the mean is $10$ and the median is $12$. If you add a value of $30$ to the set, how do the mean and median change?

There are 100 tickets in a raffle, and 5 of them are winning tickets. What is the probability of choosing a winning ticket?

A spinner has 4 equal sectors: Yellow, Blue, Red, and Green. What is the probability of landing on either Yellow or Blue?

A number is chosen at random from 1 to 20. What is the probability that the number ends in the digit 5?

A fair six-sided die is rolled. What is the probability of rolling a number greater than 6?

An event has a probability of $0.2$. If the trial is repeated 80 times, what is the expected frequency of the event occurring?

Two fair six-sided dice are rolled. What is the probability that both dice show the same number (a double)?

A number is chosen at random from the integers 1 to 20. What is the probability that the number is a factor of 20?

Three students (X, Y, and Z) are to be seated in a row of three chairs. What is the probability that they are seated in alphabetical order from left to right?

If $P(A) = 0.3$ and $P(B) = 0.4$, and events $A$ and $B$ are independent, what is the probability that neither $A$ nor $B$ occurs?

A bag contains $6$ red and $4$ blue balls. If two balls are drawn at random without replacement, what is the probability that both are red?

In a bag of $25$ sweets, $5$ are lemon flavored. What is the probability of picking a lemon sweet?

A box has $20$ cards numbered $1$ to $20$. What is the probability of picking the number $13$?

If you flip a coin, what is the probability of getting heads, expressed as a decimal?

A number is chosen at random from the set $\{2, 4, 6, 8, 10\}$. What is the probability that the number is $7$?

Two coins are tossed. What is the probability of getting exactly one head?

In a group of $40$ people, $25$ like swimming and $20$ like running. $10$ people like both. What is the probability that a person chosen at random likes only swimming?

A card is drawn from a standard deck. What is the probability that it is a Queen of Diamonds?

A box contains $10$ items, $3$ of which are defective. If a sample of $2$ items is selected at random without replacement, what is the probability that at most one item is defective?

A letter is chosen at random from the word 'PROBABILITY' and another from 'STATISTICS'. What is the probability that both letters are the same?

In a class of $20$, $12$ students are girls. If $2$ students are chosen to be representatives, what is the probability that at least one is a boy?

What is the mode of the following data: blue, red, blue, green, blue?

A card is drawn from a standard deck of $52$. What is the probability of drawing an Ace?

The number of goals a player scores in a season is:

Find the median of: $1, 10, 100$.

A class interval is $20 \le x < 30$ with a frequency of $15$. What does the number $15$ represent?

What is the probability of rolling a sum of $2$ when rolling two standard six-sided dice?

A dataset has values $2, 2, 3, 5, 8$. What is the difference between the mean and the mode?

If the mean of $x_1, x_2, ..., x_n$ is $\bar{x}$, what is the mean of $2x_1+3, 2x_2+3, ..., 2x_n+3$?

A continuous variable $h$ represents height. If $150 \le h < 160$ has a frequency of $20$ and the total frequency is $100$, what is the frequency density of this class if the class width is $10$?

In a frequency table of shoe sizes (discrete), the sizes are $36, 37, 38, 39, 40$ with frequencies $2, 5, 10, 8, 5$. What is the mode?

Find the range of the following numbers: $\{5, 15, 2, 20, 8\}$.

In a box plot, the whiskers represent the data outside of which range?

If a value is the $25^{th}$ percentile, what percentage of values are greater than it?

What is the $IQR$ of $\{10, 10, 10, 10, 10\}$?

Find $Q_3$ for the set of test scores: $65, 70, 75, 80, 85, 90, 95, 100$.

Find $Q_1$ for the set of test scores: $65, 70, 75, 80, 85, 90, 95, 100$.

If the Interquartile Range of a set is $0$, what can you conclude about the middle $50\%$ of the data?

What happens to the $IQR$ if you multiply every value in a data set by $-2$?

A frequency distribution has total frequency $N = 60$. The cumulative frequency for the first three classes is 12, 25, and 48. In which class does the median lie?

Given $Q_1 = 15$ and $Q_3 = 25$, calculate the upper outlier boundary.

What is the lower quartile of the following sorted data set: $2, 4, 6, 8, 10, 12, 14, 16$?

The interquartile range (IQR) is used to measure:

If the cumulative frequency for a score of $70$ is $45$ out of a total of $50$, how many people scored more than $70$?

How many quartiles divide a data set into four equal parts?

Which component of a box-and-whisker plot is most sensitive to a single extremely high value added to the data set?

If the median of a cumulative frequency distribution of $500$ people is $45$, how many people have a value less than $45$?

In a box plot, the median is $15$, the lower quartile is $10$ and the upper quartile is $25$. What is the IQR?

A set of data is: 5, 7, 8, 10, 12, 15, 20. If 20 is changed to 100, which of the following measures will change the most?

Which of the following statistics can be determined directly from a cumulative frequency graph but NOT directly from a standard box-and-whisker plot?

A dataset of 80 values has a maximum of 95. The box plot shows $Q_3 = 70$ and $Q_1 = 50$. Using the $1.5 \times IQR$ rule, is the maximum value an outlier?

If a line of best fit is drawn through data points representing 'age of a tree' ($x$) and 'height of the tree' ($y$), the slope would likely be:

Why is a scatter plot useful in statistics?

A line of best fit is $y = -0.5x + 10$. What is the $y$-value when $x = 4$?

The correlation between 'number of umbrella sales' and 'depth of puddles' is likely:

A scatter plot representing bivariate data has a mean point of $(\bar{x}, \bar{y}) = (6, 14)$. A student draws a line of best fit that passes through this mean point and also through the data point $(9, 23)$. What is the equation of this line of best fit?

Which of these is the most likely correlation coefficient for height and shoe size in humans?

A line of best fit is $y = -4x + 100$. If $x$ increases by $5$, how much does $y$ change?

A line of best fit is $y = 1.2x + 4$. If the mean of the $x$-values is $10$, find the mean of the $y$-values.

What is the primary danger of using a line of best fit for extrapolation?

A data set with a correlation coefficient $r = 0.9$ is transformed by adding $10$ to every $x$-value. What is the new correlation coefficient?

Which of the following is true for any set $A$?

If $A = \{x | x^2 = 9, x > 0\}$, what is the roster form of $A$?

If $U$ is the set of all integers and $E$ is the set of even integers, what is $E'$?

Which symbol represents a subset that is not necessarily equal to the other set?

Let $A$ be the set of letters in the word 'PROBABILITY' and $B$ be the set of letters in the word 'STATISTICS'. Find the value of $n(A \cap B)$.

If $A = \{1, 2, 3\}$ and $B = \{4, 5, 6\}$, then $n(A \times B)$ is:

Find the intersection of the set of factors of 12 and the set of factors of 15.

If $A = \{x : x \in \mathbb{N}, x < 5\}$ and $B = \{3, 4, 5, 6\}$, find $(A \cup B) - (A \cap B)$.

Let $U = \{x \in \mathbb{Z} : 1 \leq x \leq 20\}$. Let $A$ be the set of even numbers and $B$ be the set of multiples of 5. Find $n(A \cup B)$.

Let $A = \{1, 2, 3\}$. What is the total number of subsets of $A$?

Which operation is represented by the shaded region where two circles in a Venn diagram overlap?

If $n(\xi) = 25$ and $n(A) = 10$, find $P(A')$.

In the notation $n(A) = 5$, what does the '$n$' stand for?

A Venn diagram shows $n(A \cap B) = 2$, $n(A) = 10$, and $n(B) = 12$. What is $n(B \text{ only})$?

If $n(A \cup B) = 50$, $n(A) = 30$, and $n(A \cap B) = 10$, find $n(B)$.

In a group of 40 people, 15 play the piano, 20 play the guitar, and 10 play both. How many people play neither instrument?

Let $U = \{1, 2, 3, 4, 5, 6, 7, 8\}$, $A = \{1, 2, 3, 4\}$, and $B = \{3, 4, 5, 6\}$. Find $n((A \cap B)')$.

In a group of 50 students, 28 play basketball and 32 play soccer. If every student plays at least one of the two sports, how many play both?

If $n(A \cup B) = 100$, $n(A \cap B) = 20$, and $n(A \cap B') = 50$, find $n(B)$.

In a survey of 120 people, 80 use WhatsApp and 60 use Telegram. If 20 people use neither, find the number of people who use only Telegram.

A coin is tossed and then a spinner with 3 colors is spun. How many outcomes are in the sample space?

If you roll a 6-sided die, how many outcomes are in the event 'rolling a prime number'?

A spinner has 8 equal sections numbered 1 to 8. What is the size of the sample space?

What is the probability of rolling a '7' on a standard six-sided die?

Two standard dice are thrown. What is the probability that the sum is 11 or 12?

A bag contains 3 red candies and 2 green candies. You take one candy, eat it, and then take another. What is the probability that you ate one of each color?

How many different outcomes are possible when flipping a coin 4 times?

A tree diagram is used to represent picking two balls from a bag of 3 red, 2 blue, and 5 green balls with replacement. What is the probability that both balls are of the same color?

Two dice are rolled. Find the probability that the sum is an odd number greater than 8.

In a bag of 5 red and 5 blue marbles, two marbles are drawn without replacement. What is the probability that the first is red and the second is blue?