1.
For the data 2, 5, 7, 7, 9, 11, 15, find the median.
[2 marks]
- Ordered already, middle value
- Final answer: 7
JD SCIENCE
Statistics
Indicative marking points. Award marks for equivalent scientific or mathematical wording. Do not issue this sheet with the student worksheet.
2.
Find the mode of that data set.
[1 mark]
- Most frequent
- Final answer: 7
3.
Find the range of that data set.
[1 mark]
- Largest − smallest
- Final answer: 13
4.
Find the mean of that data set. Give your answer to 1 d.p. if needed.
[2 marks]
- Sum ÷ 7
- Final answer: 8.0
5.
The mean of four numbers is 10. Three of the numbers are 7, 9 and 12. Find the fourth number.
[3 marks]
- Total = 40
- Final answer: 12
6.
Which average is most affected by an outlier: mean, median or mode? Explain.
[2 marks]
- Mean
- It uses every value
7.
A frequency table: 1,2,3,4,5 scored by 4, 6, 7, 3, 0 students.
(a) [2 marks]
- 20
(b) [3 marks]
- (1×4+2×6+3×7+4×3)/20 = 2.45
8.
From the same table, find the modal score and the median score.
[3 marks]
- 20 values, 10th and 11th both in the 3 group
- Final answer: Mode 3; median 3
9.
Explain the difference between a bar chart and a histogram.
[3 marks]
- Bar chart: gaps, frequencies of categories
- Histogram: no gaps, frequency density, continuous data
10.
A histogram has a class 10 ≤ t < 20 of width 10 and frequency 16. Find the frequency density.
[2 marks]
- f ÷ class width
- Final answer: 1.6
11.
A scatter graph shows a strong negative correlation. Describe what this means in context if the variables are age of a car and value.
[2 marks]
- As age increases, value decreases
- Strong: points close to a line
12.
Why does correlation not imply causation? Give an exam-style example.
[2 marks]
- A third variable may be involved
- e.g. ice cream sales and drowning both rise in summer
13.
Stem-and-leaf: 1 | 2 5 ; 2 | 0 3 7 8 ; 3 | 1 4. Find the median and the range.
[3 marks]
- 9 values, 5th is 27; 34−12
- Final answer: Median 27; range 22
14.
Quartiles for 11 ordered values: find the positions of Q1, Q2 and Q3.
[2 marks]
- Final answer: Q1 = 3rd, Q2 = 6th, Q3 = 9th
15.
A data set has Q1 = 4, Q3 = 12. Find the interquartile range and explain what it measures.
[3 marks]
- Spread of the middle 50%
- Final answer: IQR = 8
16.
An outlier is often defined as a value more than 1.5 × IQR above Q3 or below Q1. If Q1 = 10, Q3 = 22, which of 42 and 40 would be outliers?
[3 marks]
- IQR = 12, fence = 22 + 18 = 40
- 42 is an outlier; 40 is on the fence / check the definition used
17.
Two groups: A has mean 20 from 10 people, B has mean 30 from 20 people. Find the combined mean.
[3 marks]
- (200 + 600)/30
- Final answer: 26.67 or 80/3
18.
Describe how to draw a box plot from a five-number summary.
[3 marks]
- Min, Q1, median, Q3, max
- Box from Q1 to Q3, line at median, whiskers to min/max
19.
Compare two box plots: team A has a higher median but a larger IQR than team B. Write a comparison in context of test scores.
[3 marks]
- A typically scored higher
- A's scores are more spread out
20.
Grouped data: 0–10 fd=2, 10–20 fd=5, 20–40 fd=3. The second class is 10 wide. Find its frequency.
[2 marks]
- 5 × 10
- Final answer: 50
21.
What is frequency density and why is it used in a histogram with unequal class widths?
[2 marks]
- Frequency ÷ class width
- So area represents frequency
22.
A pie chart represents 180 students. The 'walk' sector is 80°. How many students walk?
[2 marks]
- 80/360 × 180
- Final answer: 40
23.
In a sample of 40, 7 people own a cat. Estimate how many own a cat in a town of 12 000, assuming the sample is representative.
[2 marks]
- 7/40 × 12000
- Final answer: 2100
24.
Give one reason a sample might not be representative, and one way to improve it.
[2 marks]
- Bias / too small / only one location
- Random sample / larger / stratified
25.
Explain the difference between discrete and continuous data. Give an example of each.
[2 marks]
- Discrete: counted, e.g. number of siblings
- Continuous: measured, e.g. height
26.
Moving average: sales 4, 8, 6, 10. Calculate the 3-point moving averages.
[3 marks]
- (4+8+6)/3=6, (8+6+10)/3=8
- Final answer: 6, 8
27.
What is the purpose of a moving average on a time series?
[2 marks]
- Smooth seasonal variation
- Show the trend
28.
Amira records 5, 7, a, 9. The mean is 8. Find a.
[2 marks]
- 31 − 21 = 10? 5+7+9=21, 32−21=11
- Final answer: 11
29.
A cumulative frequency graph is drawn for 80 times.
(a) [1 mark]
- Read the time at cf = 40
(b) [2 marks]
- Times at cf 20 and 60, subtract
30.
A student says the mean of 1, 2, 3, 100 is a good typical value. Critique this.
[2 marks]
- 100 is an outlier
- Median 2.5 is more typical
31.
On AQA statistics questions, you are often asked to compare distributions. Write the two things you must compare.
[2 marks]
- Average (median/mean)
- Spread (range/IQR)
32.
Index numbers: price in year 0 is £2.50 (index 100). Year 1 price is £3.00. Find the index number for year 1.
[2 marks]
- 3/2.5 × 100
- Final answer: 120