Measures of Central Tendency (Edexcel GCSE Statistics: Higher)

Here is information about the total weights of orders (in kg) handled by a delivery company.

Use linear interpolation to work out an estimate of the median weight of the parcels.

A farmer planted two varieties of wheat, A and B, in a particular region. The grouped frequency table below gives information about the heights the wheat plants grew to after 3 months.

The estimate of the mean for variety A is calculated to be 49.7 cm to 1 decimal place.

Raj thinks that the estimate of the means for variety A and variety B suggests that variety B plants are taller than variety A plants.

Is Raj correct?
You must show your working.
Give one limitation of your conclusion.

A concert venue wants to analyse the average revenue generated from ticket sales for different sections of seating at a recent event.

For the event:

• 25% of tickets sold were for the upper section at £240 each

• 30% of tickets sold were for the middle section at £360 each

• 45% of tickets sold were for the VIP section at £480 each

Jamie, Sara, and Khalid want to calculate the average ticket price.

• Jamie thinks they should find the mean of £240, £360, and £480.

• Sara thinks they should find the median of £240, £360, and £480.

• Khalid thinks they should find the weighted mean of the ticket prices.

Which one of these three averages should they use?
Give a reason for your answer.

Jamie works out that the mean of the ticket prices is £360.
Sara finds that the median of the ticket prices is £360.

Work out the weighted mean of the ticket prices for Khalid.

The table gives information about the monthly average rainfall, in millimetres, in a region over a period of five months.

The table also provides some of the chain base index numbers for the average rainfall, correct to one decimal place.

Chain base index numbers describe the monthly rainfall as a percentage of the previous month's rainfall. E.g. 102.5 means it was 2.5 % greater than the previous month.

(i) Calculate the geometric mean of the four chain base index numbers.
You must show your working.
Give your answer correct to one decimal place.

[2]

(ii) Interpret your answer.

[2]

The highest daily temperature in degrees Celsius for 7 days in November is recorded.

The mean of the 7 values is calculated to be .

The temperatures are then converted to degrees Fahrenheit using the following conversion:

The mean of the 7 values is then calculated again.

Write down an expression in terms of for the mean when degrees Fahrenheit is used.

Maya is investigating the yearly percentage increase in visitors to two popular theme parks, Aristotle Land and Bernoulli Bay.

She has obtained the annual percentage increase in visitors for Aristotle Land for the years 2016 to 2020 and the annual percentage increase for Bernoulli Bay for the years 2017 to 2020.

The table below gives this information:

Maya concludes that the average annual percentage increase in attendance for Bernoulli Bay over the 4 years is greater than the average annual percentage increase for Aristotle Land over the 5 years.

By using appropriate geometric means, assess Maya’s conclusion.
You must show your working.

The table shows information about the number of pages that each member of "SME Book Club" read in one day.

(i) Use linear interpolation to find an estimate of the median number of pages read by the 46 members of SME Book Club.

[3]

(ii) A magazine report states that the average member of any book club reads approximately 116 pages each day.

Compare the number of pages read by the 46 members of SME Book Club with the number of pages read by the average member of any book club.

State a limitation of your comparison.

[2]

Dr. Ali is analysing the average heart rate of patients recorded by three doctors during a fitness study. Each doctor has a different number of patients, and Dr. Ali has recorded the mean heart rate for each doctor's patients.

The table below gives some information about the data.

Dr. Ali plans to use one of the following two methods to calculate the overall average heart rate for all patients across the three doctors.

Method 1
Calculate the mean of 72, 78, and 66.

Method 2
Given that Dr. Ali knows the value of , calculate the weighted mean heart rate for the three doctors.

For each of these two methods, assess whether or not the method is an appropriate way to calculate the overall average heart rate of all the patients.

The weighted mean heart rate for the three doctors’ patients is 74.2 beats per minute, correct to one decimal place.

Calculate the value of .