Topic 10: Represent Data with Exercises

What is DATA?
A collection of cats, such as numbers, words, measurements, observations or even just descriptions of things.

Data can be 'Qualitative' and 'Quantitative'

Qualitative data is describes something (describes information)
Quantitative data is describing the numbers (numerical information)

Quantitative data can also be 'Discrete' or 'Continuous'

Discrete data can only take certain values (Like whole numbers)

Continuous data can take any value (within a range)

A simple way to remind: Discrete data is counted

                                        Continuous data is measured

Example 1:

What do we know about Arrow the dog?

Qualitative:

- He is brown and black

- He has long hair

-He has lots of energy

Quantitative: 

-Discrete:

- He has 4 legs

- He has 2 brothers

-Continuous:

- He weights 25.5 kg

- He is 565 mm tall

Example 2:

A person;s height: could be any value (within the range of human heights), not just certain fixed heights.

Also a dog's weight and the length of a leaf.

Example 3:

The number of students in a class (You can't have half  a student).

The results of rolling 2 dice:

Can only have the values 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12.

Here is the video of the Qualitative and Quantitative data:

Here also another video of the Discrete and Continuous data:

-EXERCISE-

!GOOD LUCK!

Question 1: 

 Which one of the following is continuous data

a) She has two eyes.

b) She has five kittens.

c) She has four paws.

d) She weighs 5.4 kg.

Question 2:

The population of a particular classroom at any given.

a) Discrete

b) Continuous

Question 3:

The level of water in a measuring,

a) Continuous

b) Discrete

TALLY

What is Tally?

A way of keeping count by drawing marks.

Every fifth mark is drawn across the previous 4 marks, so you can easily see groups of 5

Tally Marks is easy to do a tally, just put marks on a piece of  paper!

Here are the tally marks for 1 to 4:

But the 5th mark is drawn ACROSS the previous 4 marks:

Then continue to making single marks again:

Remember: every fifth mark is drawn across the previous 4 marks

It makes it easy to see the total later on!

Example 1: A tally of 12

You can see there are two 5s (making 10) plus another 2 singles, making 12

Example 2: "What is your favorite color?"

Ask some people what their favorite color is.

Put a mark next to the color they like

When you are done, you can write in the totals.

Result: 4 people liked Yellow, 5 liked Red, 6 liked Blue, only 1 liked Green and 4 people liked Pink.

The most popular color was Blue.

What results would you get? Try this survey!

Example 3:

 Here is the video of Tally:

-EXERCISE-

!GOOD LUCK!

Question 1:

Abby counted the different colored cars that passed the school gate in 5 minutes with the following results:

Red, Black, Green, Red, White, Blue, Yellow, Red, White, Blue

Make a tally of Abby's results.

How many blue cars did he see?

Question 2:

Betty recorded the letters of the alphabet in a sentence with the following results:

T H E S U N S E T I N T H E W E S T

Betty recorded the letters of the alphabet in a sentence with the following results:

Make a tally of Betty's results.

How many S's did she record?

Question 3:

Daisy did a survey of the numbers of brothers and sisters for each the children in her class with the following results:

0, 1, 5, 3, 6, 4, 0, 0, 1, 2, 3, 1, 0, 1, 5, 4, 2, 1, 3, 3, 2, 1, 0, 1

Make a tally of Daisy's results.

How many children had no brothers or sisters?

BAR CHART

What is Bar Chart?

A Bar Chart is a graphical display of data using bars of different heights.

This is the kind of survey of your friends to find which kind of movie they liked best:

Table: Favorite Type of Movie
Comedy	Action	Romance	Drama	SciFi
4	5	6	1	4

We can show that on a bar graph like this:

It is a really good way to show relative sizes: we can see which types of movie are most liked, and which are least liked, at a glance.

We can use bar graphs to show the relative sizes of many things, such as what type of car people have, how many customers a shop has on different days and so on.

Example 1: Nicest Fruit

A survey of 145 people asked them "Which is the nicest fruit?":

Fruit:	Apple	Orange	Banana	Kiwifruit	Blueberry	Grapes
People:	35	30	10	25	40	5

And here is the bar graph:

That group of people think Blueberries are the nicest.

Bar Graphs can also be Horizontal, like this:

Example 2: Student Grades

In a recent test, this many students got these grades:

Grade:	A	B	C	D
Students:	4	12	10	2

And here is the bar graph:

Example 3:  Scores on die

The bar graphs shows the results when a die thrown a number of times. 6 gets 3 thrown, the highest is 2 which it got 6 thrown and the lowest is 3 which get only 1 thrown.

FREQUENCY DIAGRAM & FREQUENCY POLYGON

Frequency diagrams and polygons

This frequency diagram shows the heights of 200 people:

You can construct a frequency polygon by joining the midpoints of the tops of the bars.

Frequency polygons are particularly useful for comparing different sets of data on the same diagram.

Constructing a frequency polygon

HISTOGRAM

What is Histogram?

A graphical display of data using bars of different heights.

It is familiar

Example 1: Height of Orange Trees

You measure the height of every tree in the orchard in centimeters (cm)

The heights vary from 100 cm to 340 cm

You decide to put the results into groups of 50 cm:

• The 100 to just below 150 cm range,
• The 150 to just below 200 cm range,
• etc...

So a tree that is 260 cm tall is added to the "250-300" range.

And here is the result: You can see (for example) that there are 30 trees from 150 cm to just below 200 cm tall

The horizontal axis is continuous like a number line: 

Example 2: How much is that puppy growing?

Each month you measure how much weight your pup has gained and get these results:

0.5, 0.5, 0.3, −0.2, 1.6, 0, 0.1, 0.1, 0.6, 0.4

They vary from −0.2 (the pup lost weight that month) to 1.6

Put in order from lowest to highest weight gain:

−0.2, 0, 0.1, 0.1, 0.3, 0.4, 0.5, 0.5, 0.6, 1.6

You decide to put the results into groups of 0.5:

• The −0.5 to just below 0 range,
• The 0 to just below 0.5 range,
• etc...

And here is the result: There are no values from 1 to just below 1.5, but we still show the space:

The range of each bar is also called the Class Interval

In the example above each class interval is 0.5

Histograms are a great way to show results of continuous data, such as:

• weight
• height
• how much time
• etc.

Frequency Histogram What is a Frequency Histogram? It is a special histogram that uses vertical columns to show frequencies (how many times each score occurs):

Here I have added up how often 1 occurs (2 times), how often 2 occurs (5 times), etc, and shown them as a histogram.