Handling Data: Statistics

Making sense of data

Statistics is about turning a pile of numbers into something you can understand and act on. It runs from collecting the data to reading what it tells you. This module works through the whole picture: - Collecting and showing data: tables, bar charts, pie charts and line graphs.\n- Averages: the mean, the median and the mode, and when each is useful.\n- Spread: the range and the interquartile range.\n- Patterns: scatter graphs and the correlation between two sets of data. Probability has its own module. Here the focus is entirely on statistics: describing and interpreting data.

Words for handling data

Five terms you need before you use them. Learn what each one means.

Match each average to how you find it

Mean against median

The mean and the median are both averages, but they behave differently when the data has a few unusually high or low values. Knowing which to choose is a real skill.

Which average is best here?

A shop records house prices and a few of them are extremely high. Which average best describes a typical price?

• The median, because it is not distorted by the few very high values
• The mean, because it always gives the fairest picture
• The mode, because there is always one clear most common price
• The range, because it shows a typical value

Tap the two measures of spread

Tap the TWO quantities that measure the spread of data rather than an average.

• The range
• The interquartile range
• The mean
• The mode

Choosing the right chart

The chart should suit the kind of data. Picking the wrong one hides the pattern rather than showing it. Use a bar chart to compare separate categories, such as favourite sports. Use a pie chart to show how a whole is split into proportions. Use a line graph to show how something changes over time, such as temperature across a day. Use a scatter graph when you want to see whether two quantities are linked, such as hours revised and test score. The shape of the points then tells you whether there is a link, and how strong it is.

Pick the true facts about data

Select the TWO statements that are true.

• The mode is the value that appears most often
• A scatter graph can show correlation between two quantities
• The range is a type of average
• The median is always larger than the mean

Order how to run a data investigation

Put the stages of a data investigation in a sensible order.

• Write a question to investigate
• Collect the data using a suitable sample
• Organise the data in a table
• Show the data in a suitable chart
• Interpret the results and draw a conclusion

What a scatter graph reveals

Follow how a class investigated whether revision time is linked to exam success.\n\nThe data: each student recorded the hours they revised and the score they got, and every student became one point on a scatter graph. The pattern: the points sloped upward from left to right, so students who revised for longer tended to score higher. That upward slope is a positive correlation. The line of best fit: a straight line drawn through the middle of the points summed up the trend and made it easy to read. A prediction: reading up from six hours to the line and across gave an estimated score, showing how a scatter graph can be used to predict as well as to describe.

Complete the averages facts

An average found by adding all the values and dividing by the count is the _____. The middle value of the ordered data is the _____. The value that appears most often is the _____. The difference between the largest and smallest value is the _____.

Find the missing value

The mean of four numbers is 7. Three of the numbers are 5, 8 and 6. Work out the fourth number. First find the total by multiplying the mean by four, then subtract the three numbers you already know.

Build a statistics point

Choose the words that complete this statement about handling data.

Handle the data decision

Read each situation and choose the best statistical decision, then think about why.

• You have a small data set with one very large outlier and you want a typical value. Which average is most suitable?
• You want to compare the favourite colours chosen by a class. Which chart is most suitable?
• You plot hours revised against test score and the points rise together from left to right. What does this suggest?

Explain how to handle and interpret data

A classmate missed the lessons on statistics. Explain how to handle and interpret data using what this module has covered.

• Explain how to find the mean, the median and the mode
• Explain what the range tells you about the data
• Explain when the median is a better choice than the mean
• Explain what a scatter graph can show
• Finish by explaining one way to display data in a chart