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Statistics and data

Summarise and compare data using averages, spread, frequency tables and basic charts.

12 free questions · Notes · Worked solutions

Practise this topic

What you will practise

  • Calculate mean, median, mode and range.
  • Use frequency tables to calculate averages.
  • Compare distributions using averages and spread.
  • Interpret grouped data and cumulative frequency information carefully.

Revision notes

Averages

The mean is total divided by count. The median is the middle value after sorting. The mode is the most frequent value; a data set may have more than one or no mode.

Spread

Range=max−min and is sensitive to extreme values. The interquartile range is Q3−Q1 and describes the spread of the middle half. Averages and spread together give a fuller comparison.

Frequency tables

For values x with frequencies f, total frequency is Σf and mean is Σfx/Σf. For grouped intervals, a midpoint estimate can be used, but it is only an estimate.

Common checks

Sort values before finding median or quartiles. Frequency counts, not the number of table rows, determine the denominator. State units where the data has units.

A worked example

Five quiz scores are 4, 7, 7, 8 and 9. Find the mean, median, mode and range.

  1. Sum=4+7+7+8+9=35; mean=35/5=7.
  2. The ordered middle value is 7, so median=7.
  3. The most frequent score is 7, so mode=7.
  4. Range=9−4=5.

Mean 7; median 7; mode 7; range 5

Try it yourself

These are original practice questions, not official past-paper questions. Practice points count correct final answers; working is not automatically assessed.

Choose a question to begin.
Question 1 · Standard1 practice point

Find the mean of 2, 4, 6 and 8.

Need a hint?

Add the values and divide by four.

Worked solution
  1. Sum=20.
  2. Mean=20÷4=5.
Question 2 · Standard1 practice point

Find the median of 3, 10, 5, 8, 4 after ordering them.

Need a hint?

Sort first, then select the middle value.

Worked solution
  1. Ordered data: 3,4,5,8,10.
  2. The middle value is 5.
Question 3 · Standard1 practice point

For data 2, 2, 3, 5, 7, what is the mode?

Need a hint?

Which value occurs most often?

Worked solution
  1. 2 occurs twice; every other value occurs once.
  2. The mode is 2.
Question 4 · Standard1 practice point

Find the range of 11, 4, 9, 15.

Need a hint?

Subtract the smallest value from the largest.

Worked solution
  1. Largest=15 and smallest=4.
  2. Range=15−4=11.
Question 5 · Foundation1 practice point

Find the mean of 6, 8, 10 and 12.

Need a hint?

Find the total, then divide by four.

Worked solution
  1. Total=36.
  2. Mean=36÷4=9.
Question 6 · Standard2 practice points

Find the median of 2, 9, 4, 7, 5, 1.

Need a hint?

Sort the six values and average the two middle values.

Worked solution
  1. Ordered: 1,2,4,5,7,9.
  2. Middle values are 4 and 5.
  3. Median=(4+5)/2=4.5.
Question 7 · Standard2 practice points

The values 1, 2 and 3 have frequencies 2, 3 and 1 respectively. Find the mean to 2 decimal places.

Need a hint?

Use Σfx divided by Σf.

Worked solution
  1. Weighted total=1×2+2×3+3×1=11.
  2. Total frequency=2+3+1=6.
  3. Mean=11/6≈1.83 to 2 decimal places.
Question 8 · Foundation1 practice point

Find the range of temperatures 18°C, 23°C, 16°C, 21°C and 19°C.

Need a hint?

Find maximum minus minimum.

Worked solution
  1. Maximum=23°C, minimum=16°C.
  2. Range=23−16=7°C.
Question 9 · Standard2 practice points

A data set has 10 values and mean 12. What is the total of all values?

Need a hint?

Rearrange mean=total/count.

Worked solution
  1. Total=mean×count.
  2. Total=12×10=120.
Question 10 · Standard2 practice points

Five numbers have mean 8. Four numbers are 5, 7, 9 and 10. Find the fifth number.

Need a hint?

Find the required total, then subtract the known values.

Worked solution
  1. Required total=5×8=40.
  2. Known total=5+7+9+10=31.
  3. Missing value=40−31=9.
Question 11 · Stretch3 practice points

A class has 12 students with a mean height of 150 cm and 8 students with a mean height of 160 cm. Find the combined mean height.

Need a hint?

Combine total heights, then divide by 20 students.

Worked solution
  1. First group total=12×150=1800 cm.
  2. Second group total=8×160=1280 cm.
  3. Combined mean=(1800+1280)/20=154 cm.
Question 12 · Foundation2 practice points

For the ordered data 2, 3, 4, 7, 8, 10, 12, find the median.

Need a hint?

There are seven values, so the fourth is the middle.

Worked solution
  1. The values are already ordered.
  2. The fourth value is 7.

Coverage and sources

Selected IGCSE concepts, with a mix of introductory and more demanding questions. Check your own specification. AI drafted; independent teacher review is pending. Editorial details.

Cambridge IGCSE Mathematics 0580 syllabus

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