Coaching Centre
Random variables and frequency tables
Categorical, discrete and continuous variables, frequency and relative frequency tables, relative frequency as an estimate of probability, histograms and polygons, and the mode.
Types of variables
- Categorical: values are categories, such as favourite transport.
- Discrete numerical: countable values, such as the number of siblings.
- Continuous numerical: measured values on a continuous scale, such as height or time.
Frequency tables
Twenty students were asked how many siblings they have.
| Siblings $x$ | 0 | 1 | 2 | 3 | 4 | Total |
|---|---|---|---|---|---|---|
| Frequency $f$ | 3 | 8 | 5 | 3 | 1 | 20 |
| Relative frequency | 0.15 | 0.4 | 0.25 | 0.15 | 0.05 | 1 |
Discrete data is graphed with a frequency histogram (columns centred on each score, touching) or a frequency polygon (joining the tops of the columns at their centres). Categorical data uses a bar chart with gaps.
Using the table, estimate how many of the $400$ students in the school have exactly $2$ siblings.
Using the siblings table, how many students were surveyed?
$3 + 8 + 5 + 3 + 1$.
Find the mode of the siblings data.
Frequency $8$ is the highest.
Find the relative frequency of $2$ siblings.
$\dfrac{5}{20}$.
The number of siblings is:
It is counted.
The time taken to run 100 m is:
It is measured.
Favourite way to get to school is:
The values are categories.
Estimate how many of $400$ students have exactly $2$ siblings.
$0.25 \times 400$.
Find the relative frequency of having at least $3$ siblings.
$\dfrac{3 + 1}{20}$.
The relative frequencies in a table always:
$\sum \dfrac{f}{n} = \dfrac{n}{n}$.
New numbers every time. Keep going until you get five in a row.