Quartiles, Percentiles and Cumulative Frequency: Paper 2 multiple-choice

The box-and-whisker diagram below shows the distribution of the scores of some students in a quiz. Find the inter-quartile range of the distribution.

1. $7$
2. $15$
3. $21$
4. $35$

The box-and-whisker diagram below shows the distribution of the numbers of tokens collected by some children in a game. If the inter-quartile range of the distribution is a quarter of its range, find $m$.

1. $195$
2. $231$
3. $255$
4. $270$

Which of the following can be obtained from any box-and-whisker diagram?

I. Median
II. Mean
III. Range

1. I only
2. I and III only
3. II and III only
4. I, II and III

The table below shows the distribution of the numbers of siblings of 40 students.

Which of the following is true?

1. The mode of the distribution is 14.
2. The median of the distribution is 2.
3. The lower quartile of the distribution is 0.5.
4. The inter-quartile range of the distribution is 1.

The stem-and-leaf diagram below shows the distribution of the weights (in kg) of 16 workers.

If a worker is randomly selected from the group, find the probability that the weight of the selected worker is not less than the lower quartile of the distribution.

1. $\frac{1}{4}$
2. $\frac{11}{16}$
3. $\frac{3}{4}$
4. $\frac{13}{16}$

The cumulative frequency distribution table below shows the distribution of the numbers of hours (correct to the nearest hour) spent on exercise in a week by 50 adults.

How many of the adults spent 6 to 11 hours on exercise in the week?

1. $16$
2. $22$
3. $27$
4. $38$

The cumulative frequency polygon below shows the distribution of the lengths of 60 fish. Find the inter-quartile range of the distribution.

1. $10\text{ cm}$
2. $12.5\text{ cm}$
3. $15\text{ cm}$
4. $25\text{ cm}$

The cumulative frequency polygon below shows the distribution of the waiting times of 100 visitors at a museum. Estimate the 80th percentile of the waiting times.

1. $12.5\text{ minutes}$
2. $15\text{ minutes}$
3. $16\text{ minutes}$
4. $17.5\text{ minutes}$

Let $m$, $r$ and $v$ be the mode, the inter-quartile range and the variance of a group of numbers $\{x_1,x_2,x_3,\dots ,x_{10}\}$ respectively, while $m^{\prime }$, $r^{\prime }$ and $v^{\prime }$ are the mode, the inter-quartile range and the variance of the group of numbers $\{3x_1+2,3x_2+2,3x_3+2,\dots ,3x_{10}+2\}$ respectively. Which of the following must be true?

I. $m^{\prime }=3m+2$
II. $r^{\prime }=3r+2$
III. $v^{\prime }=9v$

1. I and II only
2. I and III only
3. II and III only
4. I, II and III

It is given that $d$ is a real number. Let $S_1$ be the group of numbers $\{d-5,d-2,d,d+1,d+4,d+8\}$ and $S_2$ be the group of numbers $\{d-6,d-2,d-1,d+2,d+4,d+9\}$. Which of the following are true?

I. The means of $S_1$ and $S_2$ are equal.
II. The ranges of $S_1$ and $S_2$ are equal.
III. The inter-quartile ranges of $S_1$ and $S_2$ are equal.

1. I only
2. I and II only
3. I and III only
4. II and III only