Statistics and Probability
Averages, data representation, probability, and sampling methods.
In this topic
Averages and Spread
Three types of average: - Mean = sum of all values ÷ number of values - Median = middle value when data is ordered - Mode = most frequent value
Measures of spread: - Range = highest value - lowest value - Interquartile range (IQR) = Q3 - Q1
Key Points
- Mean uses all the data but is affected by outliers
- Median is not affected by extreme values
- Mode is the only average for categorical data
- For grouped data, use midpoints to estimate the mean
Example Questions
3Find the mean, median, and mode of: 3, 5, 5, 7, 8, 9, 12
Mean = 49/7 = 7. Median = 7 (middle value). Mode = 5 (appears twice).
[3 marks]
2The mean of 5 numbers is 8. Four of the numbers are 5, 7, 9, 11. Find the fifth number.
Total = 5 × 8 = 40. Sum of four = 32. Fifth number = 40 - 32 = 8
[2 marks]
Probability
Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain).
P(event) = number of favourable outcomes / total number of outcomes
Key rules: - P(not A) = 1 - P(A) - For independent events: P(A and B) = P(A) × P(B) - For mutually exclusive events: P(A or B) = P(A) + P(B)
Key Points
- Probabilities always sum to 1 for all possible outcomes
- Tree diagrams: multiply along branches, add between branches
- Relative frequency = experimental probability
- Expected frequency = probability × number of trials
Example Questions
1A bag contains 3 red, 5 blue, and 2 green balls. One is picked at random. Find P(blue).
P(blue) = 5/10 = 1/2
[1 mark]
2Two dice are rolled. Find the probability that the total is 7.
Combinations giving 7: (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) = 6 out of 36. P = 6/36 = 1/6
[2 marks]