Measures of location and spread

Question 1

Equations for x̄ (mean)

Location

Answer 1

x̄=Σx / n (sum of data/ n)
x̄= Σfx/ Σf

Question 2

Listed data: how to find positions of quartiles

Location

Answer 2

Q₂ = (1/2)n
Q₃ = (3/4)n
etc

Question 3

Listed data: what do if it is a decimal/whole number

Location

Answer 3

decimal - round up
whole number - find midpoint with next one

Question 4

What to do with listed data before calculating location etc

Answer 4

Order it

Question 5

What needs to be changed before calculating linear interpolation?

Location

Answer 5

• Rounded class limits need to be fixed

Question 6

Linear interpolation equation

Location

Answer 6

ex.Q₃ = start of class + (amount into class/whole class) x class width

Question 7

When is linear interpolation used?

Answer 7

For grouped data

Question 8

Interquartile range: how to calculate, benefits

Spread

Answer 8

IQR = Q₃ - Q₁

benefit - ignores extreme values

Question 9

Interpercentile range: how to calculate

Spread

Answer 9

eg. 10th to 90th IPR = P₉₀ - P₁₀

Question 10

Variance (σ²) equations

Spread

Answer 10

variance = σ²
= (Σx² / n) - (x̄²)
or for grouped data:
= (Σfx² /Σf) - (x̄²)

“mean of squares minus square of means”

Question 11

coding: if y=ax + b
what does ȳ and σᵧ

Answer 11

ȳ = ax̄ + b
σᵧ = aσₓ