Statistics

Statistics and probability make up a considerable amount of Paper 2. Questions on these two topics are often linked and appear in both sections of the paper. Students are expected to be able to draw conclusions based on statistics.

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Students need to be able to find, collect and organise data. Understand how to collect unbiased data. Be able to describe a sample and how to collect one.

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Students need to be able to represent data using suitable graphs. Be aware of the types of graphs and when to use them. Use a histogram to represent continuous data. And use a scatter plot to graph bivariate data. You need to be able to comment on distribution of data.

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Students should also be able to determine the relationship between variables using scatter plots and analyse these using correlation coefficients and a line of best fit. When describing correlation between two variables, comment on both the direction and strength of the correlation.

Example: Find the correlation coefficient for the following data. Describe the correlation.

Use your calculator to find the correlation coefficient r: r = –0.73

There is a strong, negative correlation between x and y.

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Students need to be able to analyse data numerically by calculating mean, mode, median, standard deviation, interquartile range and percentiles. You also need to be able to refer to outliers.

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Students need to be able to make decisions based on the empirical rule.

Example: The IQ of a group of 10 people was found to be normally distributed with a mean

100 with a standard deviation of 12. Find the probability that a person chosen at random has an IQ of greater than 124.

95% of the data lies within two standard deviations of the mean. Therefore,

P(76 ≤ x ≤ 124) = 0.95

From the symmetry of the normal distribution we can therefore find that P(x ≥ 124) = 0.025

● Calculate z-scores in a normal distribution. ● Inferential statistics is a recent addition to the syllabus and students are now expected to fully understand this topic. Students need to understand the terms population, sample, population/sample proportion, population/ sample mean. They also need to be familiar with the Central Limit Theorem.

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Use the margin of error formula to work out the sample size that would be required in order to estimate a population proportion to a certain accuracy.

Example: A statistician wants to conduct a survey but wants to be accurate to within

5% of the population proportion. Find the minimum sample size required. ●

Construct 95% confidence intervals for the population mean from a large sample and for the population proportion, in both cases using z tables. Practice using the appropriate formulae from page 34 of the log tables. Example: In a random sample of 50 students taking an exam, it was found that the mean mark was 48.6 with standard deviation 8.5. Calculate a 95% confidence interval for the mean score of all students who took the exam. Therefore ●

Conduct a hypothesis test on a population proportion

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Use and interpret p-values. If p < 0.05, the null hypothesis is rejected. If p ≥ 0.05, do not reject the null hypothesis. To remember this, it’s helpful to learn the phrase: “If p is low,

H0 must go”.