AS level statistics Unit 1 Edexcel

A mathematical model is a simplification of a real world situation.

Some advantages of mathematical models are:

• they are quick and easy to produce
• they can simplify a more complex situation
• they help us to improve our understanding of the real world as certain variables can readily be changed
• they enable predictions to be made about the future
• they can help provide control

Some disadvantages of mathematical models are:

• they only give a partial description of the real situation
• they only work for a restricted range of values

Variables:

Variables with numerical observations are called quantitative variables. E.g. height

Variables with non-numerical observations are called qualitative variables. E.g. hair colour

A variable that can take any value in a given range is a continuous variable. E.g. time

A variable that can take only specific values in a given range is a discrete variable. E.g.number of girls in a family

Adding a column of the running total of the frequencies in a table is called the cumulative frequency

with grouped data you will need to know:

• the groups are commonly known as classes

• you need to be able to find the class boundaries

• you need to be able to find the mid-point of a class

• you need to be able to find the class width

Mode: The mode is the value that occurs most often.

Median:

The median is the middle value when the data is put in order. If there are n observations divide n by 2.

• When n/2 is a whole number find the midpoint of the corresponding term and the term above.
• When n/2 is not a whole number round the number up and pick the corresponding term.

Mean:

The mean is the sum of all the observations divided by the total number of observations.

Mode:

This is used when data is qualitative, or quantitative with either a single mode of bimodal.It is not very informative if each value only occurs once.

Median:

This is used for quantitative data. It is usually used when there are extreme values.

Mean:

This is used from quantitative data and uses all the pieces of data. It therefore gives a true measure of the data. But it is affected by extreme values.

A grouped frequency distribution consists of classes and their related class frequencies.

Classes 30-31 32-33 34-35

For the class 32-33

Lower class boundary is 31.5

Upper class boundary is 33.5

Class width is 33.5-31.5 = 2

Class mid-point is 1/2931.5+33.5) = 32.5

The modal class is the value or classes that occurs most often.

Range: range = highest value - lowest value

Finding upper and lower quartiles:

Discrete data -

lower quartile (Q1) divide n by 4.

upper quartile (Q3) divide n by four and then multiple by 3.

Continuous data -

lower quartile (Q1) divide n by 4 and then use interpolation to find corresponding value.

upper quartile (Q3) divide n by four and multiple by three and use interpolation to find corresponding value.

Interquartile range: interquartile range = upper quartile - lower quartile