Scatter Diagrams & Correlation (Edexcel GCSE Statistics: Higher)

Richard is investigating whether the GDP per capita of a country has an effect on the life expectancy in that country.

Suggest a hypothesis Richard could use for his investigation.

Richard collected the following information about 10 countries in 2021.

Source: www.ourworldindata.org

Richard used statistical software to draw a scatter diagram for the information in the table.

Give a reason why a scatter diagram is an appropriate diagram to use.

Richard's hypothesis is that countries with a higher GDP per capita, have a higher life expectancy.

He thinks this is because more money is available to spend on healthcare.

In this investigation, which variable is the explanatory variable? Give a reason for your answer.

The scatter diagram Richard created is shown below.

Explain, giving a statistical reason, whether or not this scatter diagram supports Richard's hypothesis that countries with a higher GDP per capita, have a higher life expectancy.

For these 10 countries, the double mean point of the data is (22 126, 72.4).

Using this information, draw a line of best fit on the scatter diagram.

Using statistical software, Richard finds that the gradient of the line of best fit, when the x-axis is plotted in thousands of dollars, should be 0.326.

Interpret the gradient of the line of best fit.

Richard later finds that Qatar has a GDP per capita of $143 469 and a life expectancy of 79.3 years.

Determine how this information for Qatar fits with the relationship shown in the scatter diagram for the other countries.

Isla is investigating whether there is a relationship between the average number of hours a student spends on extracurricular activities each week, and their average academic performance (measured as a percentage).

Isla takes a random sample of 20 students from her school and creates a scatter diagram.

Explain why academic performance is the response variable for this scatter diagram.

Isla's hypothesis is that, for these students, the more time students spend doing extracurricular activities, the lower their academic performance will be.

Explain, giving a statistical reason, whether or not the scatter diagram supports Isla's hypothesis

Isla wants to draw a line of best fit on the scatter diagram. Using statistical software she obtains the following information about the students.

(i) Using this information, draw a line of best fit on the scatter diagram.

[2]

(ii) Interpret the value of the intercept of the line of best fit on the Academic performance axis.

[1]

Amina and Beth are two other students in the school.

• Amina takes part in 7.5 hours of extra curricular activities per week

• Beth takes part in 12.5 hours of extra curricular activities per week

Isla uses the scatter diagram to find an estimate for the academic performance of each of these students.

Explain which of these two estimates will be the more reliable estimate.

In a separate investigation, Isla finds a positive correlation between the number of pieces of stationery in a student's bag and their academic performance.

She concludes that as the number of pieces of stationery in a student's bag increases, this causes their academic performance to increase.

Explain whether or not this conclusion is valid.

Lucy is a film critic and wants to investigate if there is a relationship between the length of a movie and the average audience rating (out of 10).

The table below gives information collected by Lucy on 8 movies, their lengths, and their audience ratings.

Lucy's hypothesis is that the longer the movie, the higher its audience rating.

Is Lucy's hypothesis supported by the data?
You must justify your answer.

Write down one thing that Lucy could do to improve the reliability of her conclusion.

A fitness centre investigated the relationship between the number of weekly training sessions () and the improvement in cardio scores and strength scores () for a sample of their members.

The table gives the Pearson’s product moment correlation coefficient for the relationship between weekly training sessions and cardio and strength improvements, as well as the equations of the regression lines for each type of training.

Compare the relationship between weekly training sessions and cardio score improvements, with the relationship between weekly training sessions and strength score improvements.

You should refer to both the correlation coefficients and the equations of both regression lines in your comparison.

The equations of the regression lines are equated:

(i) Find the value of and round your answer to the nearest whole number.

[1]

(ii) Interpret the meaning of this value of in the given context.

[1]

A university researcher is investigating the relationship between the number of hours students spend studying per week and their final exam scores in a mathematics course.

She used statistical software to draw a scatter diagram for her data.

Give one advantage of using statistical software when representing data.

The researcher calculated correlation coefficients for her data. She obtained the following results.

(i) Describe and interpret the type of correlation represented by 0.93 in the table.

[2]

(ii) Which of the two correlation coefficients in the table represents the stronger correlation?
You must give a reason for your answer.

[1]

Figure 1 and Figure 2 show two possible scatter diagrams for the data.

Which one of these two diagrams most likely represents the data? You must give a reason for your answer.

The researcher wants to use a Pearson's product moment correlation coefficient (PMCC) to compare the test scores of male students with the test scores of female students.

Explain whether or not it is appropriate to use the PMCC to make this comparison.

Arne is researching the final position of a football team in the English Premier League and the mean number of accurate passes per match.

Suggest a diagram that Arne could draw to see if there is a relationship between the teams' final position and the mean number of accurate passes per match.

The table below gives information about the data for the 2023–2024 season that Arne used.

Calculate Spearman’s rank correlation coefficient for the information in the table.

Source: fotmob.com

Interpret your answer to part (b) in the context of Arne's research.

You should refer to the effects of any anomalous data.

Sipke suggests that Pearson’s product moment correlation coefficient should be used instead of Spearman’s rank correlation coefficient to measure the correlation between the data Arne is researching.

Discuss whether or not Sipke’s suggestion is appropriate.

Consider the data shown in the below scatter diagram.

The PMCC for this data is 0.82.

Describe how the Spearman's rank for this data would compare with 0.82.

Give reasons for your answer.

A team of scientists investigated the growth rates of two types of plants: sunflowers and bamboo.

They studied the relationship between the amount of sunlight received per day, hours, and the growth rate, centimetres per day, for each of the two types of plants.

The table below shows the equation of the regression line for the data for each of the two types of plants.

When , both equations give the same value of .

Explain what this means in context.

The equation of the regression line gives information about the relationship between hours of sunlight per day and the rate of growth for each of the two types of plant.

Using this information, compare the relationship for sunflowers with the relationship for bamboo.

A different group of scientists investigated the relationship between hours of sunlight and growth rate for a third type of plant.

They also obtained the equation of the regression line for this type of plant.

The results of the different groups of scientists are to be compared.

Give one potential limitation of doing this.