Processing and presenting data

In a nutshell

Raw scientific data is processed and presented in a logical manner.

Raw vs processed data

Raw data is recorded directly from the experiment, which is processed by calculations to give processed data. Anomalies are ignored when processing data.

Example

A student investigates the incidence of heart disease in a sample size of $500$ people. She records this raw data in a table:

People that have heart disease	People that do not have heart disease
$88$	$412$

The student wants to present the number of people with heart disease as a percentage:

$({88\over 500})\times 100 = 17.6~\%$

Percentages are a form of processed data because they are calculated from the raw data.

Averages

Averages are a form of processed data and there are three types: mean, median and mode.

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

$mean = {sum~of ~all~values\over total ~number ~of ~values}$

The median is the middle value.

The mode is the value that occurs most frequently in a set of data.

Another value that can be calculated from raw data is the range, which is the difference between the largest and smallest value.

$range = largest ~value - smallest~value$

Example

A student records how many cars that drive past her house between $4\ pm$ and $5\ pm$ during the week.

Monday - $15$ cars
Tuesday - $12$ cars
Wednesday - $15$ cars
Thursday - $11$ cars
Friday - $13$ cars

All values in ascending order:

$11, 12, 13, 15, 15$

The mode is $\underline{15}$  as $15$ occurs most frequently in the data.

The median is $\underline{13}$  because it is the middle value.

The mean is $\underline{13.2}$  but this is rounded to a whole number ( $13$ ) since there can't be $13.2$ cars:

$mean ={(11+12+13+15+15)\over5} = \underline{13.2}$

The range is $\underline{4}$ 

$range = 15-11 = \underline4$ 

Significant figures

It is important to consider the following concepts when rounding numbers according to significant figures:

PROCEDURE

1.	The first significant figure is the first non-zero digit in the value.
2.	The second significant figure is the digit after the first significant figure.
3.	The third significant figure is the digit after the second significant figure and so on.
4.	Zero digits after the first significant figure are counted as significant figures.
5.	Zero digits before the first significant figure are non-significant figures.

Example

How many significant figures are in $0.002034$ ?

$0.002034$ has four significant figures.

Round $0.3400606$ to four significant figures.

$0.3400606$ rounded to four significant figures is:

$\underline{0.3401}$

Categoric data

Data that is grouped into categories is categoric data.

Example

A student investigated the different colours of cars driving past her house. Car colour is an example of categoric data.

Continuous data

Data that can have any numerical value.

Example

A student investigated the height of students in her class. Height is an example of continuous data.

Calculating gradients

Gradients can be calculated from a linear graph, or from a tangent on a non-linear graph, using the following equation:

$gradient ={ change~in ~y\over change~in ~x }$

PROCEDURE

1.	Pick two coordinates from the line of best fit: $(x_1,y_1) ~and ~(x_2, y_2)$ .
2.	$Change~in~y = y_2 - y_1$
3.	$Change~ in ~x = x_2 - x_1$
4.	$Gradient=\dfrac{change\>in\>y}{change\>in\>x}$

Calculating rate

Rate of reaction is how much product is formed in a given time; it measures how quickly a product is produced and calculated by either:

$rate ~of~reaction = {amount~of~product~produced \over time} \\ \ \\OR \\ \ \\rate ~of~reaction={amount ~of reactant~used~up\over time}$

In a graph where time is plotted on the $x$ -axis and amount of product produced or amount of reactant used up is plotted on the $y$ -axis, the initial rate of reaction can be calculated by the gradient at $t=0$ . A tangent is drawn on the graphs at $t=0$ to calculate the gradient and therefore the rate:

$rate~of~reaction = gradient={change~in~y \over~change ~in~x}$

Example

The volume of the product produced was recorded against the time taken. Calculate the initial rate of reaction.

Biology; Working scientifically; KS4 Year 10; Processing and presenting data

A.	Volume ( $cm^3$ )
B.	Time ( $s$ )
1.	Tangent for initial rate

$(x_1,y_1) = (0,0)\\ \ \\(x_2, y_2) = (20,70)\\ \ \\ initial~rate~of~reaction = {change~in~y\over~change~in~x}\\ \ \\ initial~rate~of~reaction=\underline{3.5 ~ cm^3~s^-1}$

The initial rate of reaction is  $\underline{3.5 \, cm^3 s{^-1}}$ .

Correlation

Graphs can be used to illustrate the relationship between two variables.

Graph	Type of Correlation	Explanation
	None	There is no relationship between the variable on the $x-$ axis and the variable on the y axis. This means there is no correlation between the two variables.
	Negative	As the variable on the $x-$ axis increases, the variable on the $y-$ axis decreases. This means there's a negative correlation between the two variables.
	Positive	As the variable on the $x-$ axis increases, the variable on the $y-$ axis also increases. This means there is a positive correlation between the two variables.