2.1 Representations of Data - Topic 2 Data Presentation and Interpretation

Question 1

Qualitative variables/data:

Answer 1

non-numerical data that come in classes or categories e.g. favourite colours, makes of car

Question 2

Quantitative variables/data:

Answer 2

numerical data for which the numbers are meaningful e.g. tines to run a race, height

Question 3

Discrete data:

Answer 3

set of values of data can be listed e.g. shoe size, number of goals, number of children in family etc.

Question 4

Continuous data:

Answer 4

values can’t be listed because data can take any value in a particular range e.g. height, mass, time etc.

Question 5

What can a histogram represent?

Answer 5

• groups continuous data can be presented using histograms
• histograms show rough location, general shape of data and how spread out data is

Question 6

Formulae used for histograms:

Answer 6

area of bar = k x frequency
- k=1 is easiest value to use when drawing histogram
- if k=1 then frequency = freq. density x class width

area (k x frequency) = freq. density x class width

Question 7

2 ways of calculating frequency density for histograms:

Answer 7

frequency density = frequency / class width

frequency density = frequency / number of standard widths
- if class widths have common factor then it is often convenient to take this common factor to be the standard width
- vertical axis must be labelled accordingly e.g. frequency per ‘kg’

Question 8

How do you use number of standard widths in histograms to calculate frequency?

Answer 8

• if common denominator of class widths is 5 calculate f.d. = frequency/5
• calculate frequency per 5mins by diving frequency by number of standard units
• e.g. if class width is 10 the number of standard units would be so to find frequency per 5 minutes = frequency / 2
• area of a bar would now be area = 5 x frequency

Question 9

Histogram example:

Answer 9

Question 10

What are box/whisker plots used to show?

Answer 10

• quartiles, max and min values and any outliers
• box drawn from LQ to UQ = 50% of data

Question 11

Box/whisker plot diagram:

Answer 11

Question 12

What does the area in a bar in a histogram represent?

Answer 12

frequency

Question 13

What does cumulative frequency enable us to do?

Answer 13

• enables us to estimate how many items of data fell below any particular value
• used to estimate medians, quartiles and percentiles of the data

Question 14

How must cumulative frequencies for grouped data be plotted?

Answer 14

against the upper class boundaries

Question 15

How do you calculate the median, UQ and LQ from cumulative frequency graph?

Answer 15

• if frequency is 100
• median is 100/2 = 50th value -> look on graph what x value the 50th value has
• same for LQ and UQ

Question 16

Rules for drawing frequency polygons:

Answer 16

• calculate midpoint of each class width
• plot class frequency at midpoint for the class
• connect the plotted points using straight lines

Question 17

Frequency polygon diagram:

Answer 17

Question 18

Frequency polygon on a histogram diagram:

Answer 18

Question 19

How do we compare 2 data sets

Answer 19

Comment on:
- measure of location
- measure of spread