Quantitative Skills (AQA A Level Business): Revision Note

Correlation

• A correlation exists where there is a relationship or connection between two variables 

  • Businesses often compare two variables, such as sales volume and advertising, to establish if there is any correlation between them

• In this example, a business is investigating whether there is a correlation between the number of sales managers it employs and the volume of items it sells

Types of correlation

• A positive correlation means that as one variable increases, so does the other variable

  • A line of best fit that slopes upwards can be identified 

• A negative correlation means that as one variable increases, the other variable decreases

  • A line of best fit that slopes downwards can be identified

• No correlation means that there is no connection between the two variables

  • Therefore, it is not possible to identify a line of best fit

• Correlation does not always indicate a relationship or causation between two sets of variables

  • Businesses need to conduct research to establish whether a relationship exists, as well as the strength of that relationship

Extrapolation

• Extrapolation is the use of past data or trends to make predictions about the future by extending an existing pattern beyond the range of known figures

  • Where a line of best fit can be identified, and when causation is determined, a business can extrapolate the data to make predictions around changes to either of the variables

• Extrapolating the line of best fit in the example below, the business could predict that employing seven sales managers would likely result in sales of 46 units

• Extrapolation assumes that what has happened in the past will be the same as what will happen in the future

• However, a range of examples demonstrates that this is not always the case

  • Economic shocks

    • A business extrapolating rising sales into early 2020 could not have predicted the sudden collapse in demand caused by COVID-19 lockdowns

  • Disruptive technology

    • Extrapolating Nokia's mobile phone sales in 2006 would have predicted continued dominance

    • The launch of the iPhone the following year made that projection meaningless almost immediately

  • Market saturation

    • A product growing rapidly in its early stages will not grow forever

    • Extrapolating early sales figures for a new product would overestimate future demand once the market approaches saturation

  • Changing consumer tastes

    • Extrapolating sales of sugary energy drinks in the early 2010s would have predicted continued growth, but rising health consciousness caused many consumers to switch to alternatives

  • New competition

    • A business with a growing market share cannot assume that trend will continue if a well-resourced rival enters the market

  • One-off events

    • A retailer that had an unusually strong year due to a viral social media moment cannot extrapolate that performance, as it was not driven by an underlying trend

• Extrapolation is only reliable when market conditions remain broadly stable

  • Businesses often have no way of knowing when that stability is about to end

Index numbers

• Index numbers standardise data by expressing all values relative to a chosen starting point

  • They are used to track and compare changes in a variable — such as sales, market size or price — over time

• In business, index numbers are commonly used to analyse changes in sales performance, marketing spend and market conditions

How to calculate an index number

Formula

$\mathrm{Index}=\frac{\mathrm{Current}\mathrm{period}\mathrm{value}}{\mathrm{Base}\mathrm{period}\mathrm{value}}\times 100$

Step 1: Choose what to measure

• Decide which variable to track

• For example, monthly sales revenue, market size or average selling price

Step 2: Select a base period

• Choose a starting point — typically an earlier year — and assign it an index value of 100

• All other values are then expressed relative to this base period

Step 3: Collect the data

• Gather the values for the chosen variable across all time periods to be compared

Step 4: Calculate and interpret

• Apply the formula to each time period

• An index value above 100 means the variable has increased relative to the base period

• An index value below 100 means it has fallen

• The difference between the index value and 100 shows the percentage change from the base period

Calculating percentages and percentage change

• The ability to calculate percentages and percentage change is essential for analysing business and marketing data accurately

• These skills appear throughout the course — from market share and sales growth to profit margins and budget analysis

Calculating a percentage

• Used to express one value as a proportion of another, stated as a percentage

• Commonly used in business to calculate market share, budget allocations and sales contributions

Formula

$\mathrm{Percentage}=\frac{\mathrm{Part}}{\mathrm{Whole}}\times 100$

Calculating percentage change

• Used to measure how much a value has increased or decreased relative to its starting point

  • A positive result indicates an increase

  • A negative result indicates a decrease

Formula

$\mathrm{Percentage}\mathrm{change}=\frac{\mathrm{New}\mathrm{value}-\mathrm{Old}\mathrm{Value}}{\mathrm{Old}\mathrm{value}}\times 100$

Percentage change vs percentage points

• These two terms are often confused but they mean very different things

  • A percentage point change is the arithmetic difference between two percentages

  • A percentage change measures how much one percentage has changed relative to its original value