Nisha scored points in four basketball games. The mean is 10, the median is 13 and the range is 12.

Find the number of points she scored in each game. [3]

Eight office workers earn \(\$220,\$210,\$850,\$265,\$245,\$230,\$245,\$235\).

(a) Find the median wage. [2]

(b) Explain why the mean might not be a suitable average for these wages. [1]

The stem-and-leaf diagram gives the masses of 13 packets.

Key: 3 | 1 represents 31 g.

(a) Find the interquartile range. [3]

(b) Two packets are chosen at random. Find the probability that one has mass greater than 50 g and the other less than 50 g. [3]

The table gives test marks for a group of students.

The mean mark is 6. Find n. [3]

There are 15 giraffes. One has height 2.6 m; none is shorter than 2.5 m. Their height range is 2.3 m. More than 3 have the same height, and the modal height is 3.9 m. The incomplete stem-and-leaf diagram shows 9 giraffes.

Key: 4 | 1 means 4.1 m.

Complete the stem-and-leaf diagram for all 15 giraffes. [3]

Find the median of 5, 11, 11, 13, 17, 21. [1]

Rahul has ten scores: \(9,8,9,10,7,x,9,9,x,7\). Their mean is 8. Find the interquartile range, showing your working. [4]

A dentist has appointments for 10 patients. The stem-and-leaf diagram shows the waiting times of 8 patients.

Key: 1 | 0 means 10 minutes.

The two other patients are P and Q. The mean waiting time of all 10 is 16 minutes and the range is 26 minutes. P waits longer than Q. Find their waiting times. [4]

The stem-and-leaf diagram shows the ages of 16 adults.

Key: 3 | 2 means age 32 years.

(a) Find the mode. [1]

(b) Find the median. [1]

(c) Find the percentage aged less than 38 years. [2]

Class P test marks have lower quartile 38, median 53, interquartile range 28, range 81 and highest mark 96.

(a) Draw a box-and-whisker plot. [3]

(b) Class Q has median 49 and interquartile range 35. Make two comparisons of the distributions. [2]

The diagram shows plant heights.

(a) Find the median height. [1]

(b) Find the interquartile range. [1]

(a) Find the heaviest parcel mass. [1]

(b) Find the interquartile range. [1]

Midday temperatures (°C): \(17,21,21,18,23,22,25,19,21,17,19,18,21,24,23\).

(a(i)) Complete the temperature stem-and-leaf diagram with stems 1 and 2 and key \(1\mid7\) means 17°C. [2]

(a(ii)) Find the median temperature. [1]

(a(iii)) Find the upper quartile. [1]

(a(iv)) Find the pie-chart sector angle for days at 18°C. [2]

(b(i)) From the apple box plot, find the median. [1]

(b(ii)) Find the range. [1]

(b(iii)) Find the interquartile range. [1]

(c(i)) Estimate the mean homework time for the 200 students. [4]

(c(ii)) Regroup into \(40<t\le90\) with frequency 86 and \(90<t\le150\) with frequency 114. In a histogram the first bar is 17.2 cm high. Find the second height. [2]

Weekly exercise hours: \(5,2,1.5,3,18,4.5,2,4\).

(a) Find the median. [2]

(b) Explain why the mean may not be suitable. [1]

Four men have mean mass 97.5 kg, modal mass 101 kg and range 8 kg. Find their four masses. [3]

Heights of 50 plants:

Apple masses:

(a(i)) State the median of the first test. [1]

(a(ii)) Find its range. [1]

(a(iii)) Jais scores above 75% of the students in this test. Give a possible mark. [1]

(a(iv)) Compare the two test mark distributions. [1]

(b) Estimate the mean plant height. [4]

(c(i)) Find x in the apple table. [1]

(c(ii)) Complete the apple histogram. [2]

Write an expression for the range of k consecutive integers. [1]

(a) The plot shows plant heights in centimetres. Write down the median. [1]

(b(i)) Find the range. [1]

(b(ii)) Find the interquartile range. [1]

Gemma times children and adults completing a puzzle. The children’s times are shown on the plot.

(a) Find the interquartile range of children’s times. [2]

(b) Draw the adult box plot on the same grid: minimum 28, lower quartile 42, median 58, upper quartile 70, maximum 75 seconds. [2]

(a) Potato masses have maximum174 g, range69 g, median148 g, lower quartile121 g, and interquartile range38 g.

(a) Draw a box-and-whisker plot. [4]

(b) Calculate the mean mark from this table.

The box plot shows car speeds in km/h.

(a(i)) Find the lowest speed. [1]

(a(ii)) Find the median. [1]

(a(iii)) Find the interquartile range. [1]

(b) Another car travels400 m in18 seconds. Find its average speed in km/h. [3]

The table shows travel to work for 20 people. Which average — mean, median or mode — can be used? [1]

(a) Scores: 21,21,23,26,25,21,22,20,21,23,23,27,24,21.

(a(i)) Find the range, mode, median and mean. [6]

(a(ii)) Choose a student at random. Find the probability of a score above 24. [1]

(b) Petra’s first n test scores have mean x; her first n−1 scores have mean x+1. Find her nth score in simplest form. [3]

(c) Midday temperatures in Zedford over one year:

(c(i)) Estimate the mean. [4]

(c(ii)) Complete the histogram. [4]

The masses, to the nearest kilogram, of 11 parcels are: 24, 23, 23, 26, 25, 27, 18, 96, 16, 17, 32.

(a) Find the mode. [1]

(b) Give a reason why the mean would be unsuitable. [1]

(a(i)) Complete the scatter diagram; the first six points are plotted. [2]

(a(ii)) State the correlation type. [1]

A spelling test for 30 students gives:

(b) Find mean, median, mode and range. [7]

English test marks:

(c) The English mean is 70.3. Find x. [3]

Amber’s mean mark on five tests is 80. Four marks are 68,81,74,89.

Find the fifth mark. [2]

The graph shows hummingbirds seen by Ali and Hussein on 10 days.

(a) Find Ali’s mean daily count. [3]

(b) Find Hussein’s median daily count. [2]

(c) On which day is Hussein’s count four times Ali’s? [1]

Shahruk plays four games of golf. His scores have mean 75, mode 78 and median 77.

Work out the four scores. [3]

James is an animal doctor. The table describes cats seen during one week.

One cat weighed 4 kg. On which day did James see this cat? [2]

The original list is 7, 9, 20, 3, 9.

(a) One number is removed without changing the median or range. Write that number. [1]

(b) One number is added to the original list without changing the mode. Give a possible value. [1]

Jim’s eight test marks are 7, 8, 8, y, 6, 9, 10, 5. His mean is 7.5. Find y. [2]

Seoul midday temperatures (°C) Monday to Sunday: −4, −5, −3, −11, −8, −3, −1.

(a) Find the mode. [1]

(b) How many days have temperature below the mode? [1]

The marks 8, 4, 8, y, 9 have mean 7.2. Find y. [2]

A football team receives 3 points for a win, 1 for a draw, 0 for a loss.

(a(i)) Find the median and mode. [3]

(a(ii)) Find the pie-chart sector angle for 1-point results. [2]

(b) Estimate the mean player height. [4]

A traffic survey records the number of people in each of 125 cars.

(a) Find the range. [1]

(b) Find the median. [1]

(c) Find the mode. [1]

The temperatures in °C are −2, 2, 1, −3, −1, −2, 0.

(a) Find the difference between the highest and lowest temperatures. [1]

(b) Find the mean. [2]

Temperatures in °C: −5, −1, 3, 2, −2, 0, 6.

(a) State the lowest temperature. [1]

(b) State the range. [1]