Large Data Set (Edexcel A Level Maths: Statistics): Exam Questions

Helen believes that the random variable , representing cloud cover from the large data set, can be modelled by a discrete uniform distribution.

Write down the probability distribution for .

Using this model, find the probability that cloud cover is less than 50%.

Helen used all the data from the large data set for Hurn in 2015 and found that the proportion of days with cloud cover of less than 50% was 0.315

Comment on the suitability of Helen’s model in the light of this information.

Suggest an appropriate refinement to Helen’s model.

Magali is studying the mean total cloud cover, in oktas, for Leuchars in 1987 using data from the large data set. The daily mean total cloud cover for all 184 days from the large data set is summarised in the table below.

One of the 184 days is selected at random.

Find the probability that it has a daily mean total cloud cover of 6 or greater.

Magali is investigating whether the daily mean total cloud cover can be modelled using a binomial distribution.

She uses the random variable to denote the daily mean total cloud cover and believes that .

Using Magali’s model,

(i)  find

(ii)  find, to 1 decimal place, the expected number of days in a sample of 184 days with a daily mean total cloud cover of 7.

Explain whether or not your answers to part (b) support the use of Magali’s model.

There were 28 days that had a daily mean total cloud cover of 8.

For these 28 days, the daily mean total cloud cover for the following day is shown in the table below.

Find the proportion of these days when the daily mean total cloud cover was 6 or greater.

Comment on Magali’s model in light of your answer to part (d).

Ben is studying the Daily Total Rainfall, x mm, in Leeming for 1987.

He used all the data from the large data set and summarised the information in the following table.

Explain how the data will need to be cleaned before Ben can start to calculate statistics such as the mean and standard deviation.

Using all 184 of these values, Ben estimates and

Calculate estimates for

(i) the mean Daily Total Rainfall,

(ii) the standard deviation of the Daily Total Rainfall.

Ben suggests using the statistic calculated in part (b)(i) to estimate the annual mean Daily Total Rainfall in Leeming for 1987.

Using your knowledge of the large data set,

(i) give a reason why these data would not be suitable,

(ii) state, giving a reason, how you would expect the estimate in part (b)(i) to differ from the actual annual mean Daily Total Rainfall in Leeming for 1987.

Stav is studying the large data set for September 2015.

He codes the variable Daily Mean Pressure, , using the formula .

The data for all 30 days from Hurn are summarised by

State the units of the variable .

Find the mean Daily Mean Pressure for these 30 days.

Find the standard deviation of Daily Mean Pressure for these 30 days.

Stav knows that, in the UK, winds circulate

• in a clockwise direction around a region of high pressure

• in an anticlockwise direction around a region of low pressure

The table gives the Daily Mean Pressure for 3 locations from the large data set on 26/09/2015

The Cardinal Wind Directions for these 3 locations on 26/09/2015 were, in random order,

W     NE     E

You may assume that these 3 locations were under a single region of pressure.

Using your knowledge of the large data set, place each of these Cardinal Wind Directions in the correct location in the table.

Give a reason for your answer.

Dian uses the large data set to investigate the Daily Total Rainfall, mm, for Camborne.

Write down how a value of is recorded in the large data set.

Dian uses the data for the 31 days of August 2015 for Camborne and calculates the following statistics

Use these statistics to calculate

(i) the mean of the Daily Total Rainfall in Camborne for August 2015,

(ii) the standard deviation of the Daily Total Rainfall in Camborne for August 2015.

Dian believes that the mean Daily Total Rainfall in August is less in the South of the UK than in the North of the UK.

The mean Daily Total Rainfall in Leuchars for August 2015 is 1.72 mm to 2 decimal places.

State, giving a reason, whether this provides evidence to support Dian's belief.

Dian uses the large data set to estimate the proportion of days with no rain in Camborne for 1987 to be 0.27 to 2 decimal places.

Explain why the distribution might not be a reasonable model for the number of days without rain for a 14‐day summer event.

Helen is studying one of the qualitative variables from the large data set for Heathrow from 2015.

She started with the data from 3rd May and then took every 10th reading.

There were only 3 different outcomes with the following frequencies

State the sampling technique Helen used.

From your knowledge of the large data set

(i) suggest which variable was being studied,

(ii) state the name of outcome .

George is also studying the same variable from the large data set for Heathrow from 2015.

He started with the data from 5th May and then took every 10th reading and obtained the following

Helen and George decided they should examine all of the data for this variable for Heathrow from 2015 and obtained the following

State what inference Helen and George could reliably make from their original samples about the outcomes of this variable at Heathrow, for the period covered by the large data set in 2015.

A random sample of 15 days is taken from the large data set for Perth in June and July 1987.

The scatter diagram in Figure 1 displays the values of two of the variables for these 15 days.

Describe the correlation.

The variable on the -axis is Daily Mean Temperature measured in °C.

Using your knowledge of the large data set,

(i) suggest which variable is on the -axis,

(ii) state the units that are used in the large data set for this variable.

Stav believes that there is a correlation between Daily Total Sunshine and Daily Maximum Relative Humidity at Heathrow.

He calculates the product moment correlation coefficient between these two variables for a random sample of 30 days and obtains .

Carry out a suitable test to investigate Stav’s belief at a 5% level of significance.

State clearly

• your hypotheses

• your critical value

On a random day at Heathrow the Daily Maximum Relative Humidity was 97%.

Comment on the number of hours of sunshine you would expect on that day, giving a reason for your answer.

The partially completed box plot in Figure 1 shows the distribution of daily mean air temperatures using the data from the large data set for Beijing in 2015.

An outlier is defined as a value

• more than below or

• more than above

The three lowest air temperatures in the data set are 7.6 °C, 8.1 °C and 9.1 °C.

The highest air temperature in the data set is 32.5 °C.

Complete the box plot in Figure 1 showing clearly any outliers.

Using your knowledge of the large data set, suggest from which month the two outliers are likely to have come.

Using the data from the large data set, Simon produced the following summary statistics for the daily mean air temperature, °C, for Beijing in 2015

Show that, to 3 significant figures, the standard deviation is 5.19 °C.

Simon decides to model the air temperatures with the random variable

Using Simon’s model, calculate the 10th to 90th interpercentile range.

Simon wants to model another variable from the large data set for Beijing using a normal distribution.

State two variables from the large data set for Beijing that are not suitable to be modelled by a normal distribution. Give a reason for each answer.