Biology

9.3 - Processing Data - Means, Percentages, Rates & Significant Figures

7 min

note 1 of 4

What a calculation question looks like

The N5 paper often gives you readings and asks you to calculate a mean, a percentage, a percentage change, a difference, a ratio, or a rate.
The numbers are handed to you, so the marks are for the calculation itself.

A typical question

A student measured the rate of photosynthesis of some pondweed at two carbon dioxide concentrations. The rate fell from 20 bubbles per minute to 17 bubbles per minute.

Calculate the percentage change in the rate.

How it is marked

The calculation is often marked in stages:

Setting it up - Pick the right numbers out of the data and set the calculation up, here the change of 3 over the original 20.
Working it out - Get the answer right and round it to the precision the question asks for, here a 15% decrease.

Two things to remember

Include the unit - Where the answer has a unit, a right number with the unit missing is only half done.
Show your working - If you get an early value wrong but then use it correctly, you can still be credited for the later steps, as long as your working is shown. That's why you write the calculation out rather than just the final number.

Because the same handful of calculations come up, this is a reliable set of marks once you know them and how they're rounded.

note 2 of 4

Common calculations and how to do them

Six calculations cover almost every one the paper asks for.
Learn the formula and the method for each, then slot the exam's numbers straight in.

Calculation	How to do it	Worked example
Mean	Add the repeats and divide by how many there are.	Three reaction times of 42, 45, and 48 s: mean $= \frac{42 + 45 + 48}{3} = 45$ s.
Percentage	The part over the whole, times 100: $\frac{part}{whole} \times 100$ .	18 of 25 seeds germinated: $\frac{18}{25} \times 100 = 72 %$ .
Percentage change	The change over the original value, times 100: $\frac{change}{original} \times 100$ .	Rate falls from 20 to 17 bubbles per minute: $\frac{20 - 17}{20} \times 100 = 15 %$ decrease.
Difference	Subtract one value from the other.	Rate rises from 12 to 34 bubbles per minute: 34 - 12 = 22 bubbles per minute more.
Ratio	Divide both quantities by the largest number that goes into both, to give the smallest whole numbers.	15 tall plants to 5 short plants: 15 : 5 = 3 : 1.
Rate	The change divided by the time it took: $\frac{change}{time}$ .	30 cm³ of gas collected in 5 minutes: $\frac{30}{5} = 6$ cm³ per minute.

Getting the numbers the right way round

Percentage change - Always divide by the original value, not the one you ended on, and state whether it's an increase or a decrease.
Rate - The change divided by the time, with a unit of "something per minute" or "something per second".
Ratio - Written in the order the question names the two quantities, and simplified to the smallest whole numbers.

note 3 of 4

Rounding, significant figures, and precision

Once you have the answer, round it to the precision the question states - this is judged separately from getting the calculation right.
A question saying "give your answer to two significant figures" or "to one decimal place" is telling you exactly how to round.
You can do the sum perfectly and still drop a mark by leaving a long string of digits.

Significant figures vs decimal places

These are counted differently, so read carefully which one the question asks for - they don't always give the same answer.

Significant figures - Counted from the first non-zero digit. 47.316 to three significant figures is 47.3.
Decimal places - Counted after the point. 47.316 to one decimal place is also 47.3, but 6.028 to one decimal place is 6.0.

Three things to watch

Keep paired answers consistent - If a question asks for two values, round them both to the same number of decimal places or significant figures. Giving one as 1.3 and its pair as 1.25 can be marked as inconsistent rounding, even when both numbers are right.
Do not round part-way through - Carry the full figures through the calculation and round only the final answer.
Give the unit - Where the answer has a unit, an answer without it is only half done. For 150 × 0.92 = 138, the number is right, and writing cm³ after it completes the answer.

All of this rides on showing your working: if an earlier value was wrong but you rounded and used it correctly, the rounding and unit marks can still stand.

note 4 of 4

Common exam questions

Question 1

A calculation on the paper is marked in stages. What are the stages?

Select the right data and set the calculation up; work it out correctly; and round the answer to the precision the question states, giving the unit where there is one.

Question 2

Why should you always show your working in a calculation?

Because a calculation is often marked in stages, so if an early value is wrong but you use it correctly, the later marks can still count - but only if your working is written down for the marker to see.

Question 3

A cotton crop's yield rose from 40 tonnes to 52 tonnes. Calculate the percentage increase in yield.

$\frac{52 - 40}{40} \times 100 = 30 %$ increase. The change of 12 is divided by the original value, 40.

Question 4

The average plant cell is 100 µm across and the average bacterial cell is 2 µm across. Calculate how many times bigger the average plant cell is than the average bacterial cell.

$\frac{100}{2} = 50$ times bigger.

Question 5

Cell A contains 60 mitochondria and cell B contains 20. Calculate the simplest whole-number ratio of mitochondria in cell A to cell B.

60 : 20 simplifies to 3 : 1, dividing both numbers by the smaller one.

Question 6

Of 24 patients given a new treatment, 18 were cured after one course. Calculate the percentage of patients cured.

$\frac{18}{24} \times 100 = 75 %$ .

key terms

TermDefinition

MeanThe total of the values added together, divided by the number of values.

Percentage changeThe change in a value divided by the original value, multiplied by 100.

RatioA comparison of two quantities, such as 3 : 1, usually simplified to whole numbers or written in the form n : 1.

RateThe change in a quantity divided by the time it took.

Significant figuresThe number of digits in a value, counted from the first non-zero digit, which shows how precisely it is given.

Decimal placesThe number of digits after the decimal point, which shows how precisely a value is given.

end of notes

Key points to remember

9.4 - Plotting Graphs & Bar ChartsNext up

Biology

9.3 - Processing Data - Means, Percentages, Rates & Significant Figures

7 min

note 1 of 4

What a calculation question looks like

The N5 paper often gives you readings and asks you to calculate a mean, a percentage, a percentage change, a difference, a ratio, or a rate.
The numbers are handed to you, so the marks are for the calculation itself.

A typical question

A student measured the rate of photosynthesis of some pondweed at two carbon dioxide concentrations. The rate fell from 20 bubbles per minute to 17 bubbles per minute.

Calculate the percentage change in the rate.

How it is marked

The calculation is often marked in stages:

Setting it up - Pick the right numbers out of the data and set the calculation up, here the change of 3 over the original 20.
Working it out - Get the answer right and round it to the precision the question asks for, here a 15% decrease.

Two things to remember

Include the unit - Where the answer has a unit, a right number with the unit missing is only half done.
Show your working - If you get an early value wrong but then use it correctly, you can still be credited for the later steps, as long as your working is shown. That's why you write the calculation out rather than just the final number.

Because the same handful of calculations come up, this is a reliable set of marks once you know them and how they're rounded.

note 2 of 4

Common calculations and how to do them

Six calculations cover almost every one the paper asks for.
Learn the formula and the method for each, then slot the exam's numbers straight in.

Calculation	How to do it	Worked example
Mean	Add the repeats and divide by how many there are.	Three reaction times of 42, 45, and 48 s: mean $= \frac{42 + 45 + 48}{3} = 45$ s.
Percentage	The part over the whole, times 100: $\frac{part}{whole} \times 100$ .	18 of 25 seeds germinated: $\frac{18}{25} \times 100 = 72 %$ .
Percentage change	The change over the original value, times 100: $\frac{change}{original} \times 100$ .	Rate falls from 20 to 17 bubbles per minute: $\frac{20 - 17}{20} \times 100 = 15 %$ decrease.
Difference	Subtract one value from the other.	Rate rises from 12 to 34 bubbles per minute: 34 - 12 = 22 bubbles per minute more.
Ratio	Divide both quantities by the largest number that goes into both, to give the smallest whole numbers.	15 tall plants to 5 short plants: 15 : 5 = 3 : 1.
Rate	The change divided by the time it took: $\frac{change}{time}$ .	30 cm³ of gas collected in 5 minutes: $\frac{30}{5} = 6$ cm³ per minute.

Getting the numbers the right way round

Percentage change - Always divide by the original value, not the one you ended on, and state whether it's an increase or a decrease.
Rate - The change divided by the time, with a unit of "something per minute" or "something per second".
Ratio - Written in the order the question names the two quantities, and simplified to the smallest whole numbers.

note 3 of 4

Rounding, significant figures, and precision

Once you have the answer, round it to the precision the question states - this is judged separately from getting the calculation right.
A question saying "give your answer to two significant figures" or "to one decimal place" is telling you exactly how to round.
You can do the sum perfectly and still drop a mark by leaving a long string of digits.

Significant figures vs decimal places

These are counted differently, so read carefully which one the question asks for - they don't always give the same answer.

Significant figures - Counted from the first non-zero digit. 47.316 to three significant figures is 47.3.
Decimal places - Counted after the point. 47.316 to one decimal place is also 47.3, but 6.028 to one decimal place is 6.0.

Three things to watch

Keep paired answers consistent - If a question asks for two values, round them both to the same number of decimal places or significant figures. Giving one as 1.3 and its pair as 1.25 can be marked as inconsistent rounding, even when both numbers are right.
Do not round part-way through - Carry the full figures through the calculation and round only the final answer.
Give the unit - Where the answer has a unit, an answer without it is only half done. For 150 × 0.92 = 138, the number is right, and writing cm³ after it completes the answer.

All of this rides on showing your working: if an earlier value was wrong but you rounded and used it correctly, the rounding and unit marks can still stand.

note 4 of 4

Common exam questions

Question 1

A calculation on the paper is marked in stages. What are the stages?

Select the right data and set the calculation up; work it out correctly; and round the answer to the precision the question states, giving the unit where there is one.

Question 2

Why should you always show your working in a calculation?

Question 3

A cotton crop's yield rose from 40 tonnes to 52 tonnes. Calculate the percentage increase in yield.

$\frac{52 - 40}{40} \times 100 = 30 %$ increase. The change of 12 is divided by the original value, 40.

Question 4

The average plant cell is 100 µm across and the average bacterial cell is 2 µm across. Calculate how many times bigger the average plant cell is than the average bacterial cell.

$\frac{100}{2} = 50$ times bigger.

Question 5

Cell A contains 60 mitochondria and cell B contains 20. Calculate the simplest whole-number ratio of mitochondria in cell A to cell B.

60 : 20 simplifies to 3 : 1, dividing both numbers by the smaller one.

Question 6

Of 24 patients given a new treatment, 18 were cured after one course. Calculate the percentage of patients cured.

$\frac{18}{24} \times 100 = 75 %$ .

key terms

TermDefinition

MeanThe total of the values added together, divided by the number of values.

Percentage changeThe change in a value divided by the original value, multiplied by 100.

RatioA comparison of two quantities, such as 3 : 1, usually simplified to whole numbers or written in the form n : 1.

RateThe change in a quantity divided by the time it took.

Significant figuresThe number of digits in a value, counted from the first non-zero digit, which shows how precisely it is given.

Decimal placesThe number of digits after the decimal point, which shows how precisely a value is given.

end of notes

Key points to remember

9.4 - Plotting Graphs & Bar ChartsNext up