Statistics

Calculate the median of the following numbers: $14, 15, 16, 17, 18$.

Find the range of the data set: $\{0, 25, 50, 75, 100\}$.

Find the mode of: $11, 12, 13, 11, 14, 11$.

What is the mean of $25$ and $75$?

A distribution has values $\{2, 4, 4, 6, 8, 10, 12\}$. If the value $12$ is increased to $20$, which statistic remains unchanged?

If the range of the integers $1, 3, 5, 7, 9, x$ is $10$, and $x$ is a positive integer, what are the possible values of $x$?

In a frequency table where $x$ represents the number of pets and $f$ is frequency: $x=0, f=5; x=1, f=10; x=2, f=3; x=3, f=2$. What is the median number of pets?

The mean of $1, 2, 3, ..., n$ is $\frac{6n}{11}$. Find $n$.

A set of four integers has a mean of 5, a median of 4.5, and a mode of 3. What is the range of the set?

The mean of a set of 5 numbers is 12. If the numbers are multiplied by 3 and then 5 is subtracted from each, what is the new range if the original range was 10?

In a cumulative frequency graph, we plot cumulative frequency against which value of the class interval?

If the frequencies are $2, 4, 6, 8$, which of the following is the sequence of cumulative frequencies?

For a total frequency $N=600$, the $25^{th}$ percentile is found at cumulative frequency:

If $Q_3 = 90$ and $Q_1 = 40$, what is the interquartile range?

In a dataset of 50 values, $Q_1=15$ and $Q_3=45$. If we add a new data point with a value of 100, which of the following is most likely to change significantly?

Which of the following is required to construct a cumulative frequency curve?

The marks of 80 students are summarized. The 60th percentile is 65. How many students scored more than 65 marks?

For a set of data, the median is 60 and the interquartile range is 20. If the distribution is skewed such that $Q_3 - Q_2 = 3(Q_2 - Q_1)$, find the value of $Q_1$.

A frequency distribution has 5 classes of equal width. The frequencies are 5, 10, 20, 10, 5. If the classes start at 0 and end at 50, what is the interquartile range?

A continuous variable has a cumulative frequency $F(x) = \frac{x^3}{1000}$ for $0 \leq x \leq 10$. Find the lower quartile $Q_1$.

If the frequency density is $0.25$ and the frequency is $10$, what is the class width?

What is the class width for the group $32 \le x < 40$?

If the class width is $15$ and frequency is $45$, find the frequency density.

For a histogram, if the frequency is $60$ and frequency density is $5$, the width is:

A histogram has bars of heights $2, 5, 3$ and widths $10, 10, 20$ respectively. What is the total frequency?

In a histogram, the frequency density of the class $5-15$ is $4$. What is the frequency density of the class $15-25$ if it has half the frequency of the first class?

On a histogram, the class $100-110$ has a frequency density of $2.5$. The class $110-130$ has a frequency density of $1.5$. Which class has a higher frequency?

On a frequency polygon, the area between the polygon and the x-axis is $A$. If the histogram bars from which it was derived have total area $H$, which relationship is generally true?

In a histogram, class $X$ has frequency $f$ and width $w$. Class $Y$ has frequency $3f$ and width $0.5w$. Find the ratio of the height of $X$ to the height of $Y$.

Two histograms are drawn for the same data. Histogram A uses class width $10$. Histogram B uses class width $20$. If a specific bar in A has height $H$, what is the height of the corresponding bar in B (assuming it covers two A-type classes of equal frequency)?

If the equation of the line of best fit is $y = -3x + 10$, what does the gradient tell us about the correlation?

A correlation coefficient of $r = -0.45$ is categorized as:

If $r = -1$, the relationship is described as:

On a scatter diagram, how many coordinates are represented by a single dot?

For a given set of data, the regression equation is $y = 2x + 10$. If the mean of $x$ is $\bar{x} = 5$, what is the mean of $y$ ($\bar{y}$)?

In a scatter plot, what is a 'cluster'?

If the correlation coefficient $r$ between variables $X$ and $Y$ is $0.4$, what is the correlation coefficient between $X$ and $2Y$?

Given $n=10, \bar{x}=5, \bar{y}=10, \sum x^2=300, \sum xy=600$. Find the $y$-intercept $a$ of the regression line $y = a + bx$.

A student calculates the line of regression of $y$ on $x$ as $y = -0.7x + 12$. If $S_{xx} = 100$ and $S_{yy} = 64$, find the value of $r$.

If the gradient of the regression line of $y$ on $x$ is $2.5$ and the gradient of the regression line of $x$ on $y$ is $0.1$, find the correlation coefficient $r$.

In the diagram, what is the distance between the median and the maximum value?

What is the semi-interquartile range of the dataset shown?

What value represents the $75$th percentile in this box plot?

Calculate the total range of the data using the provided diagram.

Identify the value of $k$ if $Q_1 = 10$, $Q_3 = k$, and $IQR = 25$.

Compare the whisker lengths. Which side of the distribution has the most extreme $25\%$ of data spread out over a larger range?

Determine the percentage of values between $20$ and $50$ based on the diagram.

A research group is studying the weight distribution of a specific species of bird in two different regions, A and B. The box-and-whisker plot for Region A is shown below. It is known that for Region B, the median weight is $140\text{ g}$, the interquartile range (IQR) is $30\text{ g}$, and the distribution is perfectly symmetrical. In Region A, the data set contains $n=80$ birds. Based on the diagram for Region A, which of the following statements is definitely true regarding the comparison between the two regions?

A set of data $S$ has a box plot where the whiskers are at $5$ and $25$, and the box is from $10$ to $20$. If every value in the dataset is doubled and then increased by $5$, what is the new range of the data as shown by the whiskers?

Consider a box plot representing the scores of a class of 32 students. No two students have the same score. How many students' scores are represented specifically by the line forming the upper quartile ($Q_3$)?