Types of data

There are two general types of data: qualitative data - non-numerical data such as colours of hair, makes of car quantitative data - numerical data such as marks in a test, waiting time in a doctor’s surgery.

Quantitative data may be either discrete or continuous. QUANTITATIVE DATA Discrete Data Continuous Data

Shoe sizes, such as 5, 51/2 , 6, 61/2 are discrete data. Discrete data can only take particular values. Shoe sizes, such as 5, 51/2 , 6, 61/2 are discrete data. There are no values in between. The shoe size 51/4 does not exist!

REMEMBER Each item of discrete data has an exact value.

Weight does not suddenly jump from 66 kg to 67 kg. Continuous data can take any value. Weight does not suddenly jump from 66 kg to 67 kg. It goes through all the values in between such as 66.723145...kg.

Continuous data cannot be measured exactly Continuous data cannot be measured exactly. The accuracy depends on the measuring device.

Extracting and interpreting information from tables Example : A woman wants to buy a new computer. She chooses from the models in this table. She wants a computer with at least 2 GB of memory and more than 350 GB hard drive capacity. She wants to pay less than £600. Which model should she buy?

Work through the requirements systematically. Look at the amounts of memory for each model. T9608 does not have enough. Look at the hard drive capacity. A6332 is too small. P2613 costs more than £600. So only B3413 satisfies all the requirements.

Here is an extract from a holiday brochure giving prices per person for a holiday in Palma, Majorca. Work out the cost for one person to stay for two weeks in Sunny Chalets, arriving on 1 July. Work out the cost for two people to stay for one week in Bay View Hotel, arriving on 17 June.

how many students travel to college by train? The table gives the results of a survey into the way some students travel to college. how many students travel to college by train? how many male students were surveyed? how many more female students travel to college by bus than by train? how many students were surveyed altogether?

Extracting and interpreting information from bar charts

Bar charts use bars to show patterns in data. The bars may be horizontal or vertical. Both axes should have labels and the chart should have a title. This bar chart shows some students’ marks in a maths test. The bar chart shows how many students achieved each score. This is called the frequency.

REMEMBER For continuous data there are no gaps between the bars. The vertical scale should start at 0 otherwise the differences between amounts appear larger than they are. This can be misleading. You use a dual bar chart to compare two sets of data.

This bar chart was produced by Freshco to compare the cost of a certain brand of cat food. Why is the bar chart misleading? What is the difference between the highest and lowest cost of the cat food?

This chart shows a shop’s sales in May and June this year. What is the difference between the total sales in May and the total sales in June? Which item has the biggest difference between the sales in May and the sales in June? The key shows what the different coloured bars mean.

Extracting and interpreting information from charts and graphs Pie charts show the proportion of the data that is in each category. A pie chart is split into ‘slices’ called sectors. There are 360° in a circle. To extract information from a pie chart you need to find the connection between the angles and the data.

Remember A pie chart does not give data values. A tour operator conducted a survey of its customers’ favourite holiday destinations. The pie chart displays the results of the survey. Spain was chosen by 150 people, which was 1/3 of the customers surveyed. How many customers were surveyed? How many customers chose Greece?

Pie Chart: a special chart that uses "pie slices" to show relative sizes of data Imagine you survey your friends to find the kind of movie they like best:

DRAW A PIE CHART First, put your data into a table, then add up all the values to get a total:

Next, divide each value by the total and multiply by 100 to get a percent:

Now to figure out how many degrees for each “SECTOR“ (pie slice) A Full Circle has 360 degrees

Draw a circle. Then use your protractor to measure the degrees of each sector.

YOUR TURN Here is how many students got each grade in the recent test:

Spain was chosen by 150 people, which was 1/3 of the customers surveyed. How many customers were surveyed? 1/3 of the customers surveyed is 150 people. The total number surveyed is 3/3 So the total number of customers surveyed = 3 × 150 = 450

How many customers chose Greece? You need to use a protractor to measure the angle of the sector representing Greece. The angle is 88° 360° represents 450 customers 1° represents 450/360 customers So 88° represents 88 × 450/360 = 110 customers

REMEMBER 450/360 = 1.25, but you can’t have 1.25 customers. Work out the whole calculation 88 × 450/360 in one go on your calculator.

Line graphs Line graphs are used to display continuous data. Points plotted on the graph are joined up with straight lines.

This line graph shows the temperatures in Manchester for the first five days in July. What is the difference between the highest and lowest temperatures? First identify the scale. Five small squares represent 5°C, so one small square is 1°C. From the graph, the highest temperature is 22°C and the lowest temperature is 15°C. The difference is 22 – 15 = 7.

Line Graph: a graph that shows information that is connected in some way (such as change over time) You are learning facts about dogs, and each day you do a short test to see how good you are. These are the results:

And here is the same data as a Line Graph:

Make sure to have: Vertical scale with tick marks and labels Horizontal scale with tick marks and labels Data points connected by lines A Title