Maths GCSE Interpreting and Representing Data

Overview Maths GCSE Inter­pret­ing and Rep­re­sent­ing Data

Some­one once said “there are lies, damned lies and sta­tis­tics”. Under­stand­ing how to inter­pret and rep­re­sent data gives you a chance of iden­ti­fy­ing when com­pa­nies, politi­cians, employ­ers (in fact any­one in author­ity) are using sta­tis­tics in a less than hon­est way.

To be more pos­i­tive the inter­pre­ta­tion and rep­re­sen­ta­tion of data enables you to iden­tify and solve real-life prob­lems. There are a num­ber of tech­niques. None of these tech­niques is par­tic­u­larly dif­fi­cult, you just have to prac­tice to learn them. As usual the best way for me to make sure I remem­ber each tech­nique is to:-

a) Devise a question

b) Explain the approach required to answer the question.

c) Answer the ques­tion in detail.

I find that if I have to under­stand a tech­nique well enough to set a ques­tion and explain how to answer it then I have a good chance of remem­ber­ing that tech­nique. In addi­tion, if my chil­dren ask me a ques­tion about it in the future, I will not only be able to give them the answer but also show them how to answer the ques­tion for themselves.

Stem-and-leaf Dia­grams

I had heard of stem-and-leaf dia­grams but I soon realised that I didn’t know or remem­ber how they worked. They are a sim­ple but impres­sively effec­tive way to quickly organ­ise large amounts of data.

Ques­tion

Tom believed that his par­ents did not give him enough pocket money. He decided to ask his class­mates how much pocket money per week they received. This table shows the data he collected:-

a) Use this data to pre­pare a stem-and-leaf diagram

b) How many of Tom’s class­mates receive more than £5 pocket money per week?

Approach

There is no point try­ing to describe a stem-and-leaf dia­gram, just take a peek at the answer below! Some key points to bear in mind.

• Keep it as sim­ple as pos­si­ble. The left hand col­umn (the stem) typ­i­cally has the largest sin­gle unit of mea­sure (in this exam­ple £‘s).
• Don’t try to write the fig­ures in the right-hand columns (the leaves) in ascend­ing order as this may take too long and could eas­ily result in mis­takes. The idea of a stem-and-leaf dia­gram is to quickly sort a mass of data into a man­age­able table.
•  Check the total num­ber of entries in your answer is the same as the total num­ber of data points from the orig­i­nal list.
• Make sure you include a key to show how the dia­gram should be read (see exam­ple in answer below).

Answer

a) Stem-and-leaf dia­gram of Tom’s data:-

Stem-and-leaf Dia­gram Answer