Stats - Median, Quartiles and Percentiles
Pearson Edexcel Mathematics 2022
Position formulae
What is the formula for the position of the lower quartile?
What is the formula for the position of the upper quartile?
What is the formula for the $p-th$ percentile?
Notation
Rounding rules
What are the rounding rules for the positions of medians, quartiles and percentiles?
- If it’s a whole number, it’s between the given position and the one above
- If it’s a decimal, round up to the next value
Worked positions
A data set is $255$ values long, where is the lower quartile?
At position $64$.
A data set is $255$ values long, where is the upper quartile?
At position $192$.
Linear interpolation
What assumption are you making when you perform linear interpolation?
That the data values are evenly distributed within each class.
What is interpolation?
A technique for finding an estimate of quartiles or percentiles in grouped data.
If you have a median at cumulative frequency $26$, which lies in a group ranging from $11 \to 30$, what fraction through the class are you?
What is the formula for linear interpolation in stats?
Adjusting class boundaries
Can you adjust
\[10-50 \\\\ 51-100\]
so that the class boundaries overlap, assuming the variable measured is $w$, weight?
Can you adjust
\[10-50 \\\\ 51-100\]
so that the class boundaries overlap, assuming the variable measured is $a$, age?
Why do you have to be careful adjusting class boundaries for age?
Consider that somebody is still considered 20 if it’s one day before their 21st birthday, it’s always rounded down.
What common measurement do you need to be careful adjusting class boundaries for?
Age.