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