## What you need to know

A pictograph (or pictogram) is a way of displaying data using pictures.

Example: Riley recorded how much TV she watched from Monday to Friday one week and displayed her results using a pictograph.

a) How long did Riley spend watching TV on Thursday? Give your answer in hours and minutes.

b) Over the weekend (Saturday and Sunday), Riley watched 4 times as much TV as she did on Friday. How many hours of TV did she watch over the course of the weekend?

a) In order to be understood, all pictographs must have a key. A key is the thing that here is shown to the right of the table – it tells us how to read the pictures that are shown. In this case, one picture of a TV is worth 30 minutes. From that, we can gather than two TVs must be worth 60 minutes (60 is double 30), and half a TV must be worth 15 minutes (15 is half of 30).

So, looking at Thursday, we can see that there are 3 whole TVs and 1 half TV. Therefore, the total time spent watching TV on Thursday is

(3\times 30) + 15 = 105 \text{ minutes}

105 = 60 + 45 \equiv 1\text{ hour, }45\text{ minutes}

So, the total time is 1 hour and 45 minutes.

b) We need to work out how much TV she watched on Friday. There is one whole TV and one half-TV, so we get

\text{time spent watching TV on Friday }=30+15=45\text{ minutes}

During the weekend, she watched 4 times as much:

45 \times 4=180\text{ minutes}

180 = 60 \times 3 \equiv 3\text{ hours spent watching TV on the weekend}.

Example: Faye attends a big social football club every Sunday. For 5 weeks she counted the number of people who attended and recorded the results in the table below. Draw a pictograph of Faye’s data.

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We’re going to use footballs as the picture – it’s good to use as obvious a picture as possible – so we now have to decide how many people each football will be worth. Here, we’re going to choose to have 1 football represent 20 people. This means we’re going to have to think carefully about what our pictures should look like for each week.

In weeks 2, 4, and 5, the problem is familiar. Considering whole footballs being worth 20, we know that half-footballs can be used to represent 10 people, so we get:

\text{Week 2: }60=20\times 3, \text{ so we will draw 3 footballs}

\text{Week 4: }40=20\times 2, \text{ so we will draw 2 footballs}

\text{Week 5: }70=(20\times 3)+10, \text{ so we will draw 3 footballs and 1 half-football}

However, we have to go one step further for weeks 1 and 3 and consider using a quarter of a football to represent 5 people. Doing this, we get

\text{Week 1: }55=40+15=(20\times 2)+(3\times 5), \text{ so we will draw 2 footballs and 3 quarters of a football}

\text{Week 5: }65=60+5=(20\times 3)+5, \text{ so we will draw 3 footballs and 1 quarter of a football}

Now this is done, our completed pictograph (not forgetting the key) looks like

### Example Questions

We’re going to use oranges as the picture, so we now have to decide what our key should be. In this case, we’re going to choose to make each picture of an orange worth 2 oranges.

[NOTE: If you chose to make each picture worth 1 orange, then that’s completely acceptable. As long as you constructed the pictograph correctly then there’s no problem.]

So, in week 1 there were 8 oranges eaten by Jenna’s family. 8=4\times 2, so we will have to draw 4 pictures for week 1.

In week 2 there were 9 oranges eaten. 9=4\times 2 +1, which means we will have to draw 4 whole oranges plus and extra half-orange.

Continuing this process for the other two weeks, you should get a pictograph that looks like:

a) On Tuesday there are 4 whole pictures of shoes, and on quarter of a picture. If one picture is 2km, then

\text{one quarter of a picture }=2\div 4=0.4\text{ km}

So, the distance walked on Tuesday is

(4\times 2)+(1\times 0.5)=8+0.5=8.5\text{ km}

b) 6km is her aim. Considering one picture is worth 2km, we get

6 = 2+2+2\equiv 3 \text{ pictures of shoes}

Therefore, looking at the pictograph we can see that there are 3 days – Tuesday, Thursday, and Friday – on which she achieved her goal. So, the answer is 3.

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## Home Maths Study Kit: Years 9-11 (Age 13-16)

20% OFF!- Practise papers, mark schemes and maths revision cards in every pack!
- Perfect for those in year 9, 10 and 11 studying at home
- Higher and foundation packs available
- Recommended by schools, teachers, parents and students!