Year 8 in England

7th grade statistics and probability

13 7th grade statistics and probability skills, each with a worked example, free practice that checks every answer, and a printable worksheet. Start with a mixed review, or jump to the skill you need.

Mixed review

Ten questions drawn from every skill below.

Print a review worksheet Riddle puzzle on screen Bingo

Probability of simple events

CCSS 7.SP.C.5CCSS 7.SP.C.7England: KS3 ProbabilityEngland: GCSE Foundation Probability

Example

What is the probability of rolling a number greater than 4 on a fair six-sided dice? Give a fraction in simplest form.

2 out of 6 outcomes.
P = 2/6
= 1/3

Answer: 1/3

Builds on: Equivalent fractions, Percentages, fractions and decimals

Leads to: Experimental probability and expected results, Compound events and sample spaces, Two-way tables, Describe likelihood on the 0 to 1 probability scale

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Experimental probability and expected results

CCSS 7.SP.C.6CCSS 7.SP.C.7.BEngland: KS3 ProbabilityEngland: GCSE Foundation Probability

Example

Jamal flips a drawing pin 50 times. It lands point up 10 times. What is the relative frequency of landing point up? Give a fraction in simplest form.

10/50
= 1/5

Answer: 1/5

Builds on: Probability of simple events

Leads to: Expected value, Compare experimental and theoretical probability

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Compound events and sample spaces

CCSS 7.SP.C.8England: KS3 ProbabilityEngland: GCSE Foundation Probability

Example

Two fair dice are rolled and the scores added. What is the probability the total is 8? Give a fraction in simplest form.

5 pairs add to 8.
P = 5/36

Answer: 5/36

Builds on: Probability of simple events, Multiply fractions

Leads to: Tree diagrams and Venn diagrams, Permutations and combinations, Count outcomes with lists, grids and the counting principle, Probability of two independent events

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Pie charts

England: Y6 StatisticsEngland: KS3 StatisticsEngland: GCSE Foundation Statistics

Example

In a survey of 72 people, 10 chose Dogs. What angle does Dogs get on a pie chart, in degrees?

360 ÷ 72 = 5
10 × 5 = 50°

Answer: 50

Builds on: Percentage of an amount, Angles: types and measuring

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Samples and populations

CCSS 7.SP.A.1CCSS 7.SP.A.2England: KS3 StatisticsEngland: GCSE Foundation Statistics

Example

In a random sample of 50 students, 3 said they walk to school. There are 1850 students in the school. Estimate how many walk to school.

3/50 × 1850 = 111

Answer: 111

Builds on: Proportional relationships

Leads to: Use a random sample to make predictions, Spot biased and fair samples

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Describe likelihood on the 0 to 1 probability scale

CCSS 7.SP.C.5England: KS3 Probability

Example

How likely is picking a red card from a bag of 9 red and 1 blue card?

Likely

Answer: Likely

Builds on: Probability of simple events

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Probability that an event does not happen

CCSS 7.SP.C.5CCSS 7.SP.C.7England: KS3 ProbabilityEngland: GCSE Foundation Probability

Example

The probability that it rains tomorrow is 0.11. What is the probability that it does NOT rain?

1 − 0.11 = 0.89

Answer: 0.89

Builds on: Probability of simple events

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Count outcomes with lists, grids and the counting principle

CCSS 7.SP.C.8.BEngland: KS3 ProbabilityEngland: GCSE Foundation Probability

Example

A café offers 5 wraps, 6 drinks and 2 fruit pots. A meal deal is one of each. How many different meal deals are there?

5 × 6 × 2 = 60

Answer: 60

Builds on: Compound events and sample spaces

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Probability of two independent events

CCSS 7.SP.C.8.AEngland: KS3 ProbabilityEngland: GCSE Foundation Probability

Example

A fair coin is flipped and a fair die is rolled. What is the probability of getting tails and an even number?

1/2 × 3/6 = 3/12
= 1/4

Answer: 1/4

Builds on: Compound events and sample spaces, Multiply fractions

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Compare experimental and theoretical probability

CCSS 7.SP.C.6CCSS 7.SP.C.7.BEngland: KS3 ProbabilityEngland: GCSE Foundation Probability

Example

A drawing pin is dropped 40 times. It lands point up 31 times. What is the experimental probability of landing point up? Give a fraction in simplest form.

31/40

Answer: 31/40

Builds on: Experimental probability and expected results

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Use a random sample to make predictions

CCSS 7.SP.A.2England: KS3 Statistics

Example

In a random sample of 20 students, 10 walk or cycle to school. Predict how many of the school's 460 students walk or cycle to school.

10/20 × 460 = 230

Answer: 230

Builds on: Samples and populations

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Spot biased and fair samples

CCSS 7.SP.A.1England: KS3 Statistics

Example

You want to find out which school lunch is most popular. Which sampling method is the fairest (least biased)?

Ask every 10th student on the register, across all years: everyone has an equal chance.

Answer: Ask every 10th student on the register, across all years

Builds on: Samples and populations

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Compare two groups using centre and spread

CCSS 7.SP.B.3CCSS 7.SP.B.4England: KS3 StatisticsEngland: GCSE Foundation Statistics

Example

Class A's mean height is 145 cm and Class B's is 157 cm. Both have a mean absolute deviation of 3 cm. The difference in means is how many MADs?

157 − 145 = 12
12 ÷ 3 = 4

Answer: 4

Builds on: Mean absolute deviation (MAD), Find quartiles and the interquartile range

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