Sampling and statistical diagrams

Maths · Statistics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

Test this topic free All Maths topics

The idea

A sample is a small part of a population, used to estimate facts about the whole population. A good sample is random, so every member has an equal chance of being chosen, and large enough to be reliable. A sample from one group only is biased.

Choose the diagram that fits the data. A pie chart shows shares of a whole. A time series graph shows change over time. A histogram shows grouped continuous data: the area of each bar, not its height, gives the frequency, so the vertical axis is frequency density.

A cumulative frequency graph shows a running total. Read across from the vertical axis to find the median and quartiles, or up from a value to find how many are below it.

Rules to remember

Estimate for the population = (number in sample with the feature ÷ sample size) × population size.
Pie chart angle = (frequency ÷ total frequency) × 360°.
Frequency density = frequency ÷ class width.
Frequency = frequency density × class width (the area of the bar).
Plot cumulative frequency against the upper end of each class.
For n values on a cumulative frequency graph: median at n/2, lower quartile at n/4, upper quartile at 3n/4.
Number above a value = total − cumulative frequency at that value.

Common mistake

Reading the height of a histogram bar as the frequency. The height is the frequency density, so multiply it by the class width to get the frequency.

Worked example

A histogram has a bar for 40 < h ≤ 60 with frequency density 1.5 and a bar for 60 < h ≤ 70 with frequency density 3.2. Estimate how many values are between 50 and 70.

From 50 to 60 is a width of 10 in the first bar: 1.5 × 10 = 15.
From 60 to 70 is the whole second bar, width 10: 3.2 × 10 = 32.
Total = 15 + 32 = 47.

Answer: About 47 values

Ask about this

Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.

Keep going

← Combined events and conditional probability Averages, spread and scatter graphs →Take a Maths test