M - Statistics & Mechanics 1 - 2) Measures of location and spread

Question 1

Formula for mean

Answer 1

x̄ = Σx/n

Question 2

Method to find the lower and upper quartiles of discrete data

Answer 2

1. Divide total frequency by 4 (and times by 3 for UQ)
2. If it’s a whole number, the LQ or UQ is halfway between this data point and the one above
3. If it’s not a whole number, round up and pick this data point

Question 3

Formula for variance

Answer 3

σ² = Σx²/n - x̄²

Question 4

Formula for standard deviation

Answer 4

σ = √[Σx²/n - x̄²]

Question 5

Effect on x̄ and σ when the coding is y = x + a

Answer 5

• Effect on x̄ → increase by a
• Effect on σ → no change

Question 6

Effect on x̄ and σ when the coding is y = ax

Answer 6

• Effect on x̄ → a times bigger
• Effect on σ → a times bigger