Statistics and Probability 3

In this post, I shall be cover Pictograms and Pie Charts.

PICTOGRAMS

A Pictogram, is another way of representing data. Here pictures of something are used in the form of counting tally. For Example, if the pictogram shows something about amount of sunshine each day per week, then a sun maybe used to represent say 4 hours of sunshine, in this case half a sun would be 2 hours of sunshine, a 1/4 of the sun would mean 1 hour of sunshine.

Example

Here is a pictogram of the average hours of sunshine, say per week, during winter. Let's say one sun represents 2 hours of sunshine, (this would be written as a key or legend on the actual pictogram).

How many hours of sunshines does each town recieve ?

Fineborough = 2 hours
Gammaby =  6 hours
Betatown = 10 hours
Alphaville = 6 hours + (1/2 a sun = 1 hour)
= 7 hours

Two more towns - London and Delhi recieve 9 hours and 20 hours of sun per week. Show this on the pictogram.



As you can see Delhi has 20 hours, that would equate to 10 suns. London has 9 hours, that would equate to 4 suns and half a sun !

Exercise 1

 

This pictogram above shows how many chocolate bars were sold, during a school week. 1 grid represents 8 chocolate bars sold.

1) How many Chocolate Bars were sold on each Days of the week ?

2) During a saturday school fair, the school managed to sell a 37 chocolates, how many grids would this be ?


 PIECHARTS

Piechart is another way of representing data, where each category is presented as a proportion out of the total.
We have to think of the whole piechart (whole circle) as 360 degrees. Each proportion of each category is worked out by dividing the total frequency by 360,and then multiplying each frequency by (360 divided by total frequency).This gives you the angle size of the category, draw it up using a ruler and do that for each category, remember the total angles should add up to 360 degrees.

Example

A Survey asked what methods to pupils use to get to school. Here are the results

1st step is we find the total frequency (sum) which is 90.
Then we have to find how much each angle will be for each category to do this we :

We divide 360/90 which is 4. We now have to multiply each frequency by 4 to give the angle size.
Walk = 17*4
=68 degrees
Cycle = 19*4
=76 degrees
Bus = 43*4
=172 degrees
Car = 11*4
=44 degrees

Now use a protractor to carefully draw out each catgeory as a sector of the circle :


We can see each category's percentage as a whole :

Walk = (17 / 90) *100
=19% (rounded up from 18.8)

Cycle = 21% (rounded down from 21.1)

Bus = 48% (rounded up from 47.7)
Car = 12% (rounded down from 12.2)

Exercise 2

Sarah carries out a survey from pupils. She asks them their favourite crisps flavour. Here are the results :

Favourite Crisps                 Frequency                           Angle
Plain                                             13                                             
Roast Beef                                  20                    
Chicken                                       10
Cheese & Onion                         17 

Complete the Table, and draw an accurate pie graph.