Combined means and targets, grouped data, probabilities in terms of x, picks without replacement, Venn diagrams, histograms and expected profit.
What you will learn
- Work with totals to combine or change means
- Use the fact that probabilities add to 1
- Find probabilities for two picks without replacement
- Use a histogram's area for an estimate
Think in totals
A mean hides a total.
Turn it back into one.
- 12 pupils with a mean of 60 have 12 × 60 = 720 marks altogether
- 8 more with a mean of 45 add 8 × 45 = 360
- together: 1080 ÷ 20 = 54
- for a mean of 55 with one more pupil, the total must be 55 × 21 = 1155, so they need 1155 − 1080 = 75
The range gives a missing value too. Five numbers 3, 8, 10, a and b, with 3 the smallest and b the largest, range 20 and mean 12: b = 3 + 20 = 23, the total is 5 × 12 = 60, so a = 60 − 3 − 8 − 10 − 23 = 16.
To give part of a group as a percentage, divide by the total and multiply by 100: 9 out of 36 is 9 ÷ 36 × 100 = 25%. To compare a pie chart with a count, turn the angle into a number (angle ÷ 360 × total), and compare proportions as fractions or percentages of each group, not raw counts.
The rest of this lesson and its 11 practice questions are locked.
In this lesson
- Think in totals
- Probability in steps
- Areas in a histogram
11 practice questions, marked as you go; about 30 minutes in all.
In this unit: Exam problems
The long problems that end a paper, worth 4 to 6 marks: number, algebra, ratio, geometry and statistics, Foundation and Higher, with and without a calculator, marked step by step.
- Number problems
- Algebra problems
- Ratio and rates problems
- Geometry problems
- Statistics and probability problems