Averages and measures of spread

The explanatory data set lists these numbers: 7, 2, 3, 5, 1, 2, 6, 9, 7, 2, 6, 4, 2, 3, 6.

Feb/March 2017

The values listed are 34, 38, 10, 87, 45, 28, 19, 23.

Feb/March 2017

There are 196 candidates altogether, and each one has a candidate number from 3001 up to 3196. They are arranged in numerical order in columns and rows, with 20 rows in total. The diagram shows part of the seating plan for the candidates.

Feb/March 2018

Calculate the range of the five numbers.

Feb/March 2019

The box-and-whisker plot provides data on the heights, in centimetres, of some plants.

Feb/March 2020

Calculate the mean of the marks.

Feb/March 2020

State the mode.

Feb/March 2020

The mean value of nine numbers is 17. Seven of these numbers have a total of 132. The remaining two numbers are 5 apart.

Feb/March 2021

The heights of four sisters are 1.61 m, 1.65 m, 1.53 m and 1.58 m.

Feb/March 2021

A group of students were asked how many books they had each placed in their school bags. The table contains some of the details. The mean number of books is $7.6$.

Feb/March 2021

For 14 days, the number of passengers on a bus is counted each day. 15, 18, 22, 17, 35, 38, 24, 19, 19, 24, 25, 31, 36, 29

Feb/March 2021

For a collection of six numbers, the median is $61$. The five given values are $24,\ 43,\ 58,\ 71$ and $85$.

Feb/March 2023

Over $40$ weeks, a school keeps track of how many calculators it sells in each week. The information is shown in the table.

Feb/March 2023

A reaction test was taken by 100 students. The results are listed in the table. Reaction time in seconds: 6, 7, 8, 9, 10, 11 Frequency of students: 3, 32, 19, 29, 11, 6

Feb/March 2023

Sarah notes the number of people who play golf on each of 14 days: 28, 46, 54, 71, 70, 65, 49, 50, 64, 77, 68, 72, 45, 58.

Feb/March 2024

The difference between the largest and smallest of the eight numbers is 31. Seven of the numbers are 28, 36, 42, 24, 38, 16 and 21.

Feb/March 2024

Heights were measured for 200 people. The table summarises the outcomes. Height $h$ (cm): $100 < h \le 120$, $120 < h \le 130$, $130 < h \le 150$, $150 < h \le 190$. Frequency: $32, 55, 64, 49$.

Feb/March 2024

The table gives the marks scored by each of 10 students in a test. Mark: 15, 16, 17, 18, 19, 20 Frequency: 4, 1, 2, 1, 0, 2

Feb/March 2024

The stem-and-leaf diagram gives the mass of each of 13 packets. The stems are 3, 4 and 5, and the leaves are: for 3, 1, 2, 8; for 4, 0, 1, 2, 3, 3, 8; for 5, 1, 2, 3, 4. Key: $3|1$ stands for $31$ g.

Feb/March 2025

The table presents a stem-and-leaf diagram arranged in order. Stem 0: leaves 2, A Stem 1: leaves 1, 3, B, 7 Stem 2: leaves 0, 4, 6, C Key: $1|3$ represents 13. For the ten numbers: the range is 27, the median is 16, and the mean is 16.5.

Feb/March 2025

Virat measures the height of each of $80$ sunflowers. The results are given in the table.

Feb/March 2025

The table below lists the average monthly temperatures ($^\circ$C) for Silvas, Turkey. Month: Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec Temperature ($^\circ$C): -4, -3, 2, 8, 13, 17, 19, 20, 16, 11, 8, -1

May/June 2015

The list contains the numbers 7, 9, 20, 3, 9.

May/June 2015

The Patel family travels from their home town, $H$, to Kiruna, $K$, in Lapland.

May/June 2015

The machine manufactures nails.

May/June 2015

The daily number of trains that stop at Pherlak Station over 20 days is listed below. 15 14 16 14 13 13 12 15 16 15 14 13 14 13 13 12 11 12 10 10

May/June 2015

The table gives the times, $t$ minutes, that 200 students needed to finish an IGCSE paper.

May/June 2015

The table presents the temperature recorded on each night for a week. Monday: -3^{\circ}C Tuesday: 1^{\circ}C Wednesday: -4^{\circ}C Thursday: -2^{\circ}C Friday: 5^{\circ}C Saturday: 3^{\circ}C Sunday: -1^{\circ}C

May/June 2016

Shahruk takes part in four golf games. The mean of his four scores is $75$, the mode is $78$ and the median is $77$.

May/June 2016

A garage sells used cars. The table gives the number of cars sold and the year in which they were made. Year: 2010, 2011, 2012, 2013, 2014, 2015 Frequency: 14, 13, 4, 8, 0, 11

May/June 2016

Francis asks 30 families to say how many children are in each family. The results are shown in the table: Number of children in each family: 0, 1, 2, 3, 4, 5. Number of families: 4, 6, 6, 2, 9, 3.

May/June 2017

Haroon has some items to send. Graphs and tables present information about letters and parcels.

May/June 2017

The table gives the number of customers in a restaurant on each day that it opens across one week.

May/June 2018

40 people were asked how many times they went to the cinema in one month. The table lists the results. Number of cinema visits: 0, 1, 2, 3, 4, 5, 6, 7 Frequency: 5, 5, 6, 6, 7, 3, 6, 2

May/June 2018

Find the mode from the data.

May/June 2018

The table presents the various ways 20 people travel to work.

May/June 2019

The table lists the various ways $20$ people travel to work. Method of travel: Car (10), Walk (5), Bike (3), Bus (2).

May/June 2019

On Monday, Main Street station sells 40 tickets altogether. There are four types of ticket: infant, child, adult and senior. The bar chart displays the numbers of infant, child and adult tickets sold. Bar chart text: Vertical axis labelled Frequency from 0 to 20. Horizontal axis labelled Type of ticket: Infant, Child, Adult, Senior.

May/June 2019

Mr Lester runs a fruit and vegetable shop.

May/June 2019

Kyung counts the number of people in each of 24 cars on Wednesday. His data are shown below: 1, 3, 6, 1, 2, 2, 4, 5, 3, 4, 1, 5, 3, 2, 4, 1, 1, 1, 2, 4, 4, 1, 2, 1

May/June 2019

Calculate the range, mode, median and mean for the test scores.

May/June 2019

A grouped frequency table showing the times taken by 120 boys.

May/June 2019

The stem-and-leaf diagram gives the number of hours studied last week by each of the 16 students. Stem 1 shows leaves 2 5 6 8 Stem 2 shows leaves 0 1 1 7 9 Stem 3 shows leaves 2 3 4 5 Stem 4 shows leaves 4 5 7 Key: $1|2$ means 12 hours.

May/June 2021

Emma needs to answer 15 mathematics questions. A stem-and-leaf diagram gives the time, in minutes, that she spends on each question. The stems and leaves are: 0 | 3 5 6 7 7 8 8 1 | 1 2 2 3 6 6 6 2 | 0 Key: 2 | 0 = 20 minutes.

May/June 2021

Calculate the mean for these values.

May/June 2021

The list of numbers is: 18, 28, 7, 15, 41, 19, 31, 53.

May/June 2021

The stem-and-leaf diagram gives the number of hours studied last week by each of 16 students. Stem 1: leaves 2, 5, 6, 8 Stem 2: leaves 0, 1, 1, 7, 9 Stem 3: leaves 2, 3, 4, 5 Stem 4: leaves 4, 5, 7 Key: 1|2 represents 12 hours.

May/June 2021

Emma is to complete 15 mathematics questions. The stem-and-leaf diagram shows how many minutes she needs for each question. Stem 0: leaf values 3, 5, 6, 7, 7, 8, 8 Stem 1: leaf values 1, 2, 2, 3, 6, 6, 6 Stem 2: leaf value 0 Key: $2|0 = 20$ minutes.

May/June 2021

Mei and Jian each produce a four-faced dice, as the diagram shows. The faces on each dice are marked 1, 2, 3 and 4.

May/June 2021

The mass, $m$ kg, of each of the 40 parcels in a warehouse is measured. The table gives the mass data for these parcels.

May/June 2021

Find the range of the data.

May/June 2021

Kim has a 6-sided spinner numbered 1 to 6. She spins it 63 times, and the results are recorded in the table.

May/June 2022

The following facts are given about six numbers: • The smallest number is 37. • The range equals 24. • The mode is 43. • The median is 46. • One of the numbers is a multiple of 11.

May/June 2022

Antonio runs a shop close to the beach.

May/June 2022

Maria runs a restaurant with 30 tables. On one day, she counts how many customers are seated at each table at 7 pm. A bar chart displays the findings.

May/June 2022

Finish the stem-and-leaf diagram so that it represents this data.

May/June 2022

The values listed are: 21, 8, 15, 32, 3, 29, 19, 45, 8.

May/June 2023

The stem-and-leaf diagram gives the ages of 21 people. Key: 1 | 6 shows 16 years.

May/June 2023

These are the test scores obtained by 16 students: 15, 26, 9, 45, 36, 20, 41, 39, 40, 23, 32, 18, 41, 34, 37, 31.

May/June 2023

Mika works out how many letters are in each of the 61 words in a paragraph. A few of his answers are shown in the table and bar chart.

May/June 2023

Calculate an estimate for the mean.

May/June 2023

The stem-and-leaf diagram gives the ages of the 16 workers in a shop on 1st January 2022. Key: $2|5$ stands for 25.

May/June 2024

Find the median time value.

May/June 2024

The six numbers are 0, 2, 2, 3, 4, 7.

May/June 2025

These are the lengths, in minutes, of seven phone calls: 10, 22, 5, 7, 35, 8, 75.

May/June 2025

The table presents information about the marks obtained by a group of students in a test. Test marks: 4, 5, 8. Frequencies: 2, 4, $n$. The mean mark equals 6.

May/June 2025

A die with four faces is labelled 1 to 4. Hrishi rolls the die 50 times. The outcomes are listed in a table: Number 1: Frequency 14 Number 2: Frequency 15 Number 3: Frequency 9 Number 4: Frequency 12

May/June 2025

Kai’s restaurant is open each week from Tuesday through Saturday. Over two weeks, he records the number of customers each day. The bar chart displays part of the data. The vertical axis is titled "Number of customers". The horizontal axis is titled "Day" and shows Tue, Wed, Thur, Fri and Sat. The key gives Week 1 (shaded) and Week 2 (unshaded).

May/June 2025

The heights of 140 basketball players are collected, and the results are displayed in the table. Height $h$ (cm): $160 < h \leq 180$, $180 < h \leq 185$, $185 < h \leq 190$, $190 < h \leq 200$, $200 < h \leq 210$ Frequencies: $7, 12, 31, 70, 20$.

May/June 2025

Find the median for the numbers $5, 11, 11, 13, 17, 21$.

May/June 2025

Jim obtains the following marks in 8 tests: $7, 8, 8, y, 6, 9, 10, 5$. His mean mark is $7.5$.

Oct/Nov 2015

The table presents data on the number of pets owned by $24$ students.

Oct/Nov 2015

Give a five-number set with mode $3$, median $6$ and range $5$.

Oct/Nov 2015

Jim achieves the following marks in 8 tests: $7, 8, 8, y, 6, 9, 10, 5$. His average mark is $7.5$.

Oct/Nov 2015

The table presents data on how many pets are kept by 24 students.

Oct/Nov 2015

A total of 120 children take part in an athletics competition.

Oct/Nov 2015

A total of 120 students sit a mathematics examination.

Oct/Nov 2015

Eleven children tried to solve a puzzle. The data below give the number of attempts made by each child: 7, 6, 8, 5, 6, 5, 7, 8, 3, 8, 1.

Oct/Nov 2016

The heights, in centimetres, of 8 people are: 153, 175, 168, 158, 161, 172, 164, 172.

Oct/Nov 2016

Javier spent time at a carnival with his friends.

Oct/Nov 2016

Amber’s average score over five tests is 80. Her scores in four of those tests are 68, 81, 74 and 89.

Oct/Nov 2017

Amber’s mean score over five tests is 80. Her results in four of those tests are 68, 81, 74 and 89.

Oct/Nov 2017

Find the median value.

Oct/Nov 2017

Find the median value.

Oct/Nov 2017

The table gives details of the time $t$, measured in minutes, that each of 150 girls needed to finish an essay.

Oct/Nov 2017

The numbers in the list are: 16, 7, 23, 18, 73, 20, 95, 17, 89, 54.

Oct/Nov 2018

The table gives the number of pets owned by each of the 95 students at a school.

Oct/Nov 2018

Finish the table.

Oct/Nov 2018

There are 70 people, and each one takes a driving test. Each person keeps trying the test until they pass. The table gives the results.

Oct/Nov 2018

The table gives the lengths of time, $T$ minutes, that 120 people each spend in a supermarket on one Saturday.

Oct/Nov 2018

Metal is recycled in a factory. Each week, the mass, x tonnes, is recorded. The table lists the outcomes for 52 weeks.

Oct/Nov 2018

The numbers in the list are 27, 14, 8, 93, 32, 55, 14, 38, 73, 47.

Oct/Nov 2019

On one day, each of 10 students sent these numbers of texts: 18, 13, 15, 8, 9, 17, 12, 8, 6, 14.

Oct/Nov 2019

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

Oct/Nov 2019

Each of 50 students records how many glasses of water they drink in one day. The data for 10 of the students are shown below: 2, 5, 1, 3, 2, 1, 0, 0, 1, 1.

Oct/Nov 2019

Find the median of the data.

Oct/Nov 2019

Seven numbers have a mean of $16$. The six values given are $12, 20, 19, 10, 21$ and $13$.

Oct/Nov 2020

The table gives data on the times, $t$ seconds, that each of 100 students needed to solve a puzzle.

Oct/Nov 2020

Sean serves as the manager of a museum.

Oct/Nov 2020

Find the median value.

Oct/Nov 2020