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Sem 5 Prep
← Visual AnalyticsTypes of data, and how to present them

Formulas for this chapter

Mid-value of a class interval

Mid-value = (lower limit + upper limit) / 2

Whenever a frequency distribution has to be summarised, plotted at a point, or used to compute a mean from grouped data.

lower limit
Smallest value the class contains, e.g. 10 in 10-20
upper limit
Largest value the class contains, e.g. 20 in 10-20

Cumulative frequency

CF(k) = f(1) + f(2) + ... + f(k)

For an ogive, and for any "how many are below x" or percentile question. Always check that CF of the last class equals n.

f(i)
Frequency of the i-th class
CF(k)
Cumulative frequency up to and including class k
n
Total number of observations; CF of the last class must equal it

Percentile from grouped data

Pk = L + ((k/100 x n - CF_below) / f) x c

To read a median (k = 50) or a quartile off a frequency distribution. State the convention you are using; different books place the position at kn/100 or k(n+1)/100.

L
Lower limit of the class containing the percentile
n
Total observations
CF_below
Cumulative frequency of all classes before that class
f
Frequency of that class
c
Width of that class

Pie slice angle

Angle = (category count / total) x 360 degrees

Only when a pie chart is unavoidable. The course recommends a sorted bar chart instead, because length is judged accurately and angle is not.

category count
Frequency of the category
total
Sum of all category frequencies
Step 1 of 25
The ideaTheory

Two numbers that are not both numbers

A survey records gender as 1 for male and 2 for female. It also records height in centimetres.

You can average the heights. Averaging the genders gives 1.5, which is not a person. Both columns look like numbers. Only one of them is a number.

Everything in this chapter follows from telling those two apart, because the chart you may draw depends on it.

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