Measures of Spread

Question 1

How do you calculate variance?

Answer 1

Mean of the squares [ Σx²/n ]
- Square of the mean [ (Σx/n)² ]

or Sₓₓ/n

Question 2

What is standard deviation (σ) ?

Answer 2

> How spread out values are from the mean

> root variance (σ²) OR root Sₓₓ/n

Question 3

For y = (x-a) / b, how do you code mean?

Answer 3

y̅ = (x̅ - a) / b

Question 4

For y = (x-a) / b, how do you code standard deviation?

Answer 4

σᵧ = σₓ / b

Question 5

How do you calculate interquartile range?

Answer 5

Q₃ - Q₁

Where Q₃ is UQ and Q₁ is LQ

Question 6

How do you interpolate to find quartiles or percentiles?

Answer 6

( Qₓ - C₁ ) / ( C₂ - C₁ ) = ( Fₓ - F₁ ) / ( F₂ - F₁ )

Where C₁ is the lower class boundary and C₂ is the upper class boundary and F is the corresponding cumulative frequency

⚫ ——– ⚫ ——– ⚫

These boundaries will be the midpoint between 2 classes

Question 7

How do you calculate percentile range?

Answer 7

Pᵧ - Pₓ

Where Pᵧ is the larger percentile and Pₓ is the smaller percentile

Question 8

What do you assume when using interpolation to calculate quartiles?

Answer 8

Data values are all evenly distributed and therefore the data is discrete