Statistics

Identify the range of the data set: $100, 105, 95, 110$.

The ages of four children are $3, 5, 7, 9$. What is their mean age?

Find the median of $10, 20, 30, 40$.

What is the mean of $1, 2, 3, 4, 5$?

In a distribution of $100$ observations, the median is found to be $45$. If all observations are increased by $5$, what is the new median?

The mean of $4$ numbers is $18$. Three of the numbers are $12, 15,$ and $25$. What is the $4$th number?

The mean weight of $8$ boys is $55$ kg and the mean weight of $12$ girls is $45$ kg. Find the combined mean weight.

A set of four distinct positive integers has a mean of $6$ and a median of $5.5$. What is the maximum possible range for this set?

The mean speed for a trip consisting of two equal distances is calculated using the harmonic mean. If the speeds are $40$ km/h and $60$ km/h, find the mean speed.

If the mean of $a, b, c, d, e$ is $20$, and the mean of $a, b, c$ is $15$, what is the mean of $d$ and $e$?

For the interval $12.4 < x \le 12.8$, what is the class width?

Which of the following describes a symmetrical distribution in a frequency polygon?

If the frequency of a class is $100$ and the frequency density is $2$, what is the class width?

In a frequency polygon, the points are plotted above the ________ of each class interval.

If a histogram has a frequency density of $2$ for the class $0 < x \le 10$ and $4$ for the class $10 < x \le 15$, which class has more items?

A frequency polygon point is at $(55, 22)$. If this represents the class $50 < x \le 60$, and the next class is $60 < x \le 80$, what is the next $x$-coordinate to be plotted?

The total frequency in a histogram is $200$. A bar covering $10\%$ of the total area has a width of $5$. What is its frequency density?

A grouped frequency table has classes $10-20, 20-30, 30-50$. The frequency of the first class is $15$. If the frequency densities are all equal, find the total frequency of the distribution.

A histogram has two bars. Bar 1: width $10$, frequency $30$. Bar 2: width $25$, frequency $50$. What is the ratio of the height of Bar 1 to the height of Bar 2?

In a histogram, the frequency density is $FD = f/w$. If a new class is created by doubling the frequency and halving the class width of an existing class, by what factor does the bar height change?

A cumulative frequency graph for 120 students' exam marks is shown. Estimate the number of students who scored more than 60 marks.

From the box plot, identify the median value.

Which component of the box plot indicates the degree of dispersion in the middle $50\%$ of the data?

What is the frequency of observations between $x=20$ and $x=40$ according to this cumulative frequency curve?

The median of a data set is 50. If the box plot is symmetric and the IQR is 20, what is the value of the lower quartile?

What is the frequency density for the modal class if we were to convert this cumulative frequency graph back to a histogram? (Consider interval 40 to 60)

A skewed distribution is shown in the box plot. Which statement is correct about the skewness?

A data set representing the times (in minutes) taken by 80 runners to complete a 5 km race is summarized in the cumulative frequency graph shown. It is observed that $15\%$ of the runners are classified as 'elite' because they completed the race in less than $k$ minutes. Using the cumulative frequency curve provided, which is approximated by the function $F(x) = \frac{80}{1 + e^{-0.2(x-25)}}$ for the range of the data, find the interquartile range (IQR) of the completion times.

The cumulative frequency graph shows the weights of 800 luggage items. It is found that 10% of items are overweight and require a fee. If the overweight threshold is $23$ kg, find the percentage of items that weigh between the median and $23$ kg.

In a box plot for the distribution of salaries, the whisker ends are at $20,000$ and $80,000$. The box spans from $35,000$ to $55,000$. If the salary distribution is transformed by $S_{new} = 1.1 S_{old} + 5000$, what is the new interquartile range?

In a scatter diagram, 'bivariate' means there are how many variables?

Does correlation imply causation?

If the mean of $x$ is $8$ and the mean of $y$ is $12$, the line of best fit must pass through:

A 'weak negative' correlation means the points on the scatter diagram:

A scatter diagram for $x$ and $y$ has a range of $x$ values from $20$ to $80$. A student uses the line of best fit to predict $y$ for $x = 85$. Why should this prediction be treated with caution?

The correlation between depth of a hole ($x$) and time taken to dig ($y$) is positive. If the line of best fit is $y = 4x + 10$, how long does it take to dig $5$ meters?

When drawing a line of best fit by eye on a scatter diagram, which rule is generally followed?

A scatter diagram has a strong positive correlation. A new point is added that is exactly on the existing line of best fit but very far from the other points in the positive direction. What is the effect on the correlation coefficient $r$?

For a scatter plot, if the line of best fit is $y = 5$, what is the correlation between $x$ and $y$?

If the correlation coefficient between $x$ and $y$ is $0.9$, what percentage of the variation in $y$ can be explained by the linear relationship with $x$? (Concept: $r^2$)