Representation of data + coding

Question 1

How coding affects

Answer 1

if y = ax + b:
* ȳ = ax̄ + b (both addition and multiplying affects mean)
* σᵧ = aσ (only multiplication affects variance)

Question 2

converting a cumulative frequency diagram to a box plot

Answer 2

min, Q₁, Q₂, Q₃, max = x values on a cumulative frequency graph, where y = min/ Q₁/ Q₂/ Q₃/ max

Question 3

General equations for outliers (useful to know)

Answer 3

Q₁ - 1.5 x IQR
Q₃ + 1.5 x IQR

Question 4

What type of data are histograms used for?

Answer 4

Histograms are used for continuous data

so diagram has no gaps

Question 5

Histograms: frequency density equation

Answer 5

frequency density = frequency / class width

Question 6

Histograms: area equation

Answer 6

Area = k (constant) x frequency

Question 7

What 2 things need to be commented on when making comparisons between box plot diagrams?

Answer 7

• Location - e.g. median
• Spread - e.g. range

Both in context.

Question 8

How can a frequency polygon be created from a histogram?

Answer 8

Joining the middle of the top of each bar (only if they have equal class widths)

Question 9

advantages and disadvantages of box plots

Answer 9

A:
enables median and interquartiles
spread of data can be seen easily

D:
can be easily misinterpretted
original data is not shown, individual data points

Question 10

advantages and disadvantages of cumulative frequency diagrams

Answer 10

A:
enables estimation of median and interquartiles
D:
original data is not shown, individual data points