Using mathematical data in business
Businesses use a range of mathematical data to help them understand their business and the data they gather. Common calculations used by business include calculations of percentages, percentage changes and averages.
Calculating percentages
Businesses regularly use percentages, for example if they want to find out what percentage of a selling price is profit for a product.
Percentages are displayed using the % symbol. A percentage means ‘out of 100’.
- 50% means 50 out of 100
- 12% means 12 out of 100
To change a decimal to a percentage, multiply by 100. So to change 0.67 to a percentage: 0.67 × 100 = 67%.
To work out a percentage of an amount. Divide the amount by the number you want to work it out of and then multiply by 100. For example, if a business wants to calculate the percentage of 16 out of 40: 16 ÷ 40 × 100 = 40%.
If a business was selling an item for £50, and £18 of that was profit, they can work out what percent their profit margin is on an item, 18 ÷ 50 × 100 = 36%.
Calculating percentage changes
Businesses may also want to work out percentage changes over time, for example the percentage change in demand for an item.
To work out a percentage increase there are two steps:
- Step one: work out the difference between the two numbers being compared. (Increase = New Number - Original Number)
- Step two: divide the increase amount by the original number, then multiply the result by 100 (% increase = Increase ÷ Original Number × 100)
To work out a percentage decrease there are also two steps:
- Step one: work out the difference between the two numbers being compared. (Decrease = New Number - Original Number)
- Step two: divide the decrease amount by the original number, then multipy the result by 100 (% decrease = Decrease ÷ Original Number × 100)
Percentages are usually rounded to a convenient number of decimal places, for example to the nearest percentage, or to two decimal places.
As an example, if a business made sales of 36 items one week and 54 items the next, they can calculate the percentage change by:
- Step one - 54 – 36 = 18
- Step two – 18 ÷ 36 × 100 = 50% increase
If a business made sales of 84 items one week and 52 items the next, they can calculate the percentage change by:
- Step one: 52 – 84 = -32
- Step two: -32 ÷ 84 × 100 = 38% decrease (rounded to the nearest percentage)
Calculating averages
Averages are also often used in business. For example a business may want to see their average sales or over a period of time.
An average is calculated by adding all of the values in a set together, and dividing by the number of values there are. For example, if a business wanted to work their average amount of products sold each month, over a six- month period, they would add the amounts sold each month together and divide by six. For example:
100 + 115 + 96 + 142 + 89 + 112 = 654
654 ÷ 6 = 109 average sales.
As you can see, they have added the amount of products sold each month, then divided the total by the number of months to find the average.
If a business wanted to calculate their average revenue over four months, they would do the following:
£1000 + £1250 + £900 + 1050 = £4200
£4200 ÷ 4 = £1050 average revenue.
As with percentages, averages are usually rounded to a convenient number of decimal places where necessary, for example to the nearest pound or penny.