Statistics and Probability

A researcher wants to ensure both smokers and non-smokers are represented in a health study. They divide the population into these two groups and then pick $50$ from each. This is:

What is a significant disadvantage of conducting a census for a very large population?

The speed of a cyclist during a race is an example of:

Which tool is most useful for ensuring every member of a sampling frame has a chance to be picked randomly?

If a sample is 'representative', it means:

In a systematic sample of $200$ people from a population of $2,000$, the first person chosen is the $5^{th}$ person on the list. Who is the $3^{rd}$ person chosen for the sample?

A survey asks: 'Which of the following social media platforms do you use? (Check all that apply)'. The data collected for each platform (used vs. not used) is:

A researcher wants to sample $50$ people from a crowd of $1,000$. They decide to pick the $20^{th}$ person, then the $40^{th}$, and so on. What is the probability that the $1,000^{th}$ person is selected?

A factory has two production lines. Line A produces $2,000$ items and Line B produces $3,000$ items. A stratified sample of $100$ items finds $4$ defects in the sample from Line A and $6$ from Line B. If the sample was proportional, how many items were sampled from Line B?

A survey asks: 'Given the failure of the current policy, do you support the new proposal?' What type of bias does this question introduce?

If a histogram bar has a frequency density of $4$ and a frequency of $20$, what is the class width?

On a cumulative frequency curve, the $25$th percentile corresponds to which quartile?

Which diagram is best for comparing the medians and spreads of two different data sets?

If the total number of data points is $60$, the median is located at the:

A cumulative frequency curve is used to estimate the number of people who weigh less than $70$ kg. If the curve reaches a cumulative frequency of $160$ at $x=70$, and the total number of people is $200$, how many people weigh more than $70$ kg?

In a histogram, if the frequency density of a class $20-25$ is $6$, how many data points are in that class?

If a box plot is perfectly symmetrical, which of the following must be true?

If a data set is modified by multiplying every value by $3$, how does the length of the box in a box plot change?

The class $10-30$ has a frequency density of $1.5$ and the class $30-40$ has a frequency density of $4.0$. If these are the only two classes, what is the mean of the distribution (using midpoints)?

In a cumulative frequency graph for $80$ items, the $IQR$ is $10$. If the $60^{th}$ item corresponds to $x = 45$ and the $20^{th}$ item corresponds to $x = 35$, which value represents the $75^{th}$ percentile?

Calculate the mean of the numbers: $2, 3, 4, 5, 6$.

Identify the mode of the list: $12, 14, 12, 16, 12, 18$.

What is the median of $50, 40, 60$?

Find the mean of the set: $2, 4, 6$.

If the mean of $x$ and $1/x$ is $M$, what is the mean of $x^2$ and $1/x^2$ in terms of $M$?

The mean of $40$ observations was $160$. It was detected on re-checking that the value $165$ was wrongly copied as $125$. The correct mean is:

Consider the set $\{k, 2k, 3k, 4k, 5k\}$ where $k > 0$. What is the ratio of the mean to the median?

A set of $5$ numbers has a mean of $20$. If a number $x$ is added, the mean becomes $22$. If instead of $x$, a number $y$ is added, the mean becomes $18$. Find the mean of $x$ and $y$.

If the mean of $n$ numbers is $M$, and the sum of the first $n-1$ numbers is $S$, what is the $n^{th}$ number?

A grouped data set has classes $0-4$ and $5-9$. The frequency of $0-4$ is $10$ and $5-9$ is $20$. Using the mid-value method ($2$ and $7$), find the estimated mean.

In the data set $5, 10, 15, 20, 25, 30, 35$, which value is $Q_3$?

In the data set $5, 10, 15, 20, 25, 30, 35$, which value is $Q_1$?

Which visual feature of a box plot shows the range?

If the maximum value is $90$ and the range is $70$, what is the minimum value?

A box plot shows: Min $= 2, Q_1 = 5, \text{Med} = 7, Q_3 = 10, \text{Max} = 20$. Which quartile of the data is the most spread out?

If $Q_1 = 12$ and $Q_3 = 18$, which of the following values would be considered an outlier using the $1.5 \times IQR$ rule?

Determine the $IQR$ of the set: $1, 1, 1, 1, 1, 5, 5, 5, 5, 5$.

Which of the following statistics is the most 'robust' (least sensitive) to the addition of an extreme outlier?

A data set of test scores is transformed by $y = 1.5x + 10$. If the original range was $40$ and the original $IQR$ was $15$, what are the new range and $IQR$?

Given the set of data: $\{x, x+1, x+2, x+3, x+4, x+5, x+6\}$. If the interquartile range is $4$, which method was likely used to calculate the quartiles?

A spinner is numbered $1$ to $6$. What is the probability of landing on a divisor of $5$?

A letter is chosen at random from the word $HELLO$. What is the probability that the letter is 'L'?

A number is chosen at random from the integers $1$ to $10$. What is the probability that it is a perfect square?

What is the probability of drawing a red card from a standard deck of $52$ cards?

The probability that event $E$ occurs is $P(E)$. The probability that event $E$ does not occur is $P(E')$. Which of the following is always true?

A bag has $10$ colored tiles: $3$ Red, $2$ Blue, and $5$ Yellow. If two tiles are drawn with replacement, what is the probability that both tiles are the same color?

A bag contains $3$ red balls and $n$ white balls. If the probability of drawing a red ball is $0.2$, what is the value of $n$?

Two letters are chosen from the word "ALGEBRA" without replacement. Find the probability that both are vowels.

A card is drawn from a standard deck. Let $E$ be the event 'drawing a King' and $F$ be the event 'drawing a Face card'. Find $P(E|F)$.

For two events $A$ and $B$, $P(A) = 0.25$ and $P(B) = 0.5$. If the probability that neither occurs is $0.4$, find $P(A \cap B)$.

If $n(A) = 10$, $n(B) = 12$, and $n(A \cap B) = 4$, find $n(A \cup B)$.

A tree diagram is used to find the probability of a girl having a sandwich (S) or pasta (P) for lunch on two days. If $P(S) = 0.6$ and $P(P) = 0.4$, what is the probability she has pasta on both days?

What does the symbol $\cup$ represent in set theory and Venn diagrams?

In a tree diagram with replacement, if the probability of picking a blue ball is $\frac{3}{10}$, what is the probability of picking a non-blue ball?

A tree diagram shows two stages of a process. Stage 1 has outcomes X ($0.4$) and Y ($0.6$). If X occurs, Stage 2 has outcome Z with probability $0.3$. If Y occurs, Stage 2 has outcome Z with probability $0.7$. Find $P(Z)$.

In a Venn diagram of 100 students, 40 like Math ($M$), 40 like Science ($S$), and 40 like History ($H$). The intersections are: $n(M \cap S) = 10, n(S \cap H) = 10, n(M \cap H) = 10,$ and $n(M \cap S \cap H) = 5$. How many students like none of these subjects?

Three fair coins are tossed. What is the probability of getting exactly two heads?

A marble is drawn from a bag containing 3 red, 2 yellow, and 5 blue marbles. If it is not yellow, what is the probability it is blue?

In a Venn diagram of 3 sets, the region $(A \cup B) \cap C'$ represents which of the following?

A student chooses two integers from 1 to 5 inclusive without replacement. What is the probability that the sum of the integers is even?

A survey about the best time for school to start is given only to teachers. Why might the results be misinterpreted as the opinion of the whole school?

When a graph uses small pictures of people to represent population, and one picture represents $1000$ people, what is this graph called?

A data set contains the heights of $10$ students. If the height of the teacher is added to the set, and the teacher is much taller than the students, which of the following will increase?

If a sample is chosen by picking every $10$th person on a list, it is called:

1. Data manipulation and misinterpretation: practice question 1 for Statistics and Probability?

1. Data manipulation and misinterpretation: practice question 2 for Statistics and Probability?

1. Data manipulation and misinterpretation: practice question 3 for Statistics and Probability?

1. Data manipulation and misinterpretation: practice question 4 for Statistics and Probability?

1. Data manipulation and misinterpretation: practice question 5 for Statistics and Probability?

1. Data manipulation and misinterpretation: practice question 6 for Statistics and Probability?

Which of these values could not be a correlation coefficient $r$?

The strength of a correlation is determined by:

If $y = 3x + 1$, what is the predicted value of $y$ for $x = -2$?

A line of best fit equation is $y = -0.5x + 10$. If $x$ increases by $2$ units, what happens to $y$?

If the equation of the line of best fit is $y = 0.5x - 2$, what is the predicted value of $y$ when $x = 100$?

A line of best fit has a $y$-intercept of $5$ and passes through the point $(10, 25)$. What is its gradient?

A line of best fit is $y = 2x + 1$. If the data set is $\{(1, 3), (2, 5), (3, 7)\}$, what is the mean point?

A line of best fit is $y = 0.8x + 5$. If the $x$-values represent years after 2000 (so $x=1$ is 2001), what is the predicted $y$-value for the year 2010?

In a linear regression model $y = mx + c$, if the correlation coefficient $r$ is $0$, what is the most likely value of $m$?

A data set has a mean point $(5, 15)$. Which of the following equations could represent its line of best fit?

If the $75^{th}$ percentile of a set of scores is $85$, what does this mean?

Find the median of the following list: $50, 40, 60, 30, 70$.

In a box plot, the whiskers extend to which values?

What percent of scores are between the minimum and the lower quartile?

If the $60$th percentile of a dataset is $40$, then $40$ percent of the data values are:

Which percentile corresponds to the $Q_3$?

Given the values $10, 12, 14, 16, 18, 20, 22$, what is the IQR?

1. Quartiles and percentiles: practice question 1 for Statistics and Probability?

1. Quartiles and percentiles: practice question 2 for Statistics and Probability?

1. Quartiles and percentiles: practice question 3 for Statistics and Probability?

In a study of plant growth, if 'amount of water' is the independent variable, where should it be plotted?

What is the name for the graph used to display bivariate data?

When all the points in a scatter plot lie exactly on a straight line with a negative slope, the correlation is:

A scatter plot shows that as the number of hours of exercise increases, resting heart rate generally decreases. This is a:

A scatter plot shows a strong positive correlation. If the line of best fit is $y = 3x + 5$, and a student uses it to predict $y$ for an $x$ value inside the range, the prediction is likely to be:

Describe the correlation: The more minutes you spend running on a treadmill, the more calories you burn.

When drawing a line of best fit, why should it ideally pass through the mean of both variables?

A researcher is studying the relationship between 'Exercise Time' and 'Body Fat Percentage'. They find $r = -0.82$. Which statement is the most accurate qualitative description?

If you have a set of data where $x$ and $y$ are the same variable (e.g., height measured twice for each person), what would the qualitative correlation be?

In a scatter plot, if the line of best fit has a gradient of $0$, what is the qualitative correlation?

If the relative frequency of an event is $0.75$, how many times does it occur in 12 trials?

In a sample of 40 light bulbs, 2 were defective. What is the relative frequency of a bulb being defective?

An archer hits the bullseye 24 times in 80 shots. What is the relative frequency of hitting the bullseye?

A dice is rolled 200 times and a '6' is rolled 32 times. What is the relative frequency of rolling a '6'?

In an experiment with 160 trials, the relative frequency of an outcome was $0.375$. What was the frequency of that outcome?

The relative frequency of a specific bird visiting a feeder is $0.24$. If the feeder is visited 75 times, how many times was it that specific bird?

A factory produces 2500 chips. The relative frequency of a chip being functional is $0.98$. How many functional chips are produced?

A student calculates the relative frequency of an event as $0.24$ after 250 trials. How many more trials must be performed with a $100\%$ success rate to reach a relative frequency of $0.40$?

An insurance company finds the relative frequency of claims in a year is $0.04$ for 5000 policyholders. If for a different group of 3000 policyholders the relative frequency is $0.06$, what is the relative frequency of claims for all 8000 policyholders?

A coin is tossed $N$ times. The relative frequency of heads is $0.45$. If the coin is tossed 100 more times and 55 heads are obtained, the relative frequency of heads becomes $0.47$. Find $N$.

A library sent $300$ surveys and got $90$ responses. What is the response rate?

A survey of $50$ people has a $90\%$ response rate. How many people responded?

If $70$ people are surveyed and the response rate is $10\%$, how many people responded?

A gym survey was sent to $120$ members. $30$ responded. What is the response rate?

If a response rate is $0.065$, what is this as a percentage?

A feedback link was clicked by $1,200$ people, but only $300$ actually submitted the form. What is the response rate based on the number of clicks?

A survey is sent to $750$ people. If the response rate is $28\%$, how many people did NOT respond?

A sample size of $800$ produced $160$ responses. If the sample size is increased by $200$ and the number of responses increases by $50$, what is the new response rate?

If $30\%$ of the surveys sent are returned, and of those, $10\%$ are returned by people over age $60$. If $15$ people over age $60$ responded, how many surveys were sent in total?

A survey has a $22\%$ response rate. If $110$ people responded, and each response costs the company $5$ in processing fees while each sent survey costs $1$ in postage, what is the total cost?

In a single roll of a fair die, find the probability of getting a number less than 3 or getting a 6.

If $P(A) = 0.22, P(B) = 0.33, \text{ and } P(C) = 0.44$ are mutually exclusive, what is $P(A \cup B \cup C)$?

A bag has 8 green balls and 12 yellow balls. What is the probability of not picking a green ball?

If $P(A) = \frac{2}{7}$ and $P(B) = \frac{3}{7}$ are mutually exclusive, find $P(A' \cap B')$.

A random integer between 1 and 10 (inclusive) is chosen. Let $A$ be 'the number is 1' and $B$ be 'the number is greater than 8'. Find $P(A \cup B)$.

The probability that a bus is early is 0.12, and the probability it is on time is 0.56. Find the probability it is late, assuming these are the only three possibilities.

If $P(A) = \frac{1}{8}, P(B) = \frac{1}{8}, P(C) = \frac{1}{8}$, and they are mutually exclusive, what is $P(A \cup B \cup C)$?