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Don't take a biased sample. You wouldn't go to an primary school to ask them about their driving habits.

Grouped Discrete Data

Sometimes, it's better to group the data into classes. For example:

THese are the number of customers at a restaurant during lunch hours.

Measures of Center

1. Make a tally-frequency table.

2. Make a vertical bar chart.

Organizing Data

Measures of center help us get an idea of what is "normal" for a set of data.

20 students were asked how many pets they have. Here is the raw data of the results:

Mean

- the arithmetic average of a data set

0 1 0 3 2 0 2 1 1 0

1 1 2 3 0 1 0 2 1 1

Mean =

the sum of all data values

the number of data values

=

Median

Example 1: Finding Centers of Data

1. What is the variable? Is it discrete or continuous?

- the middle value of an ordered data set

2. Display the data in a tally-frequency table.

13+1

3. Display the data in a vertical bar chart.

If n=13, then =7, so the median is the 7th value.

If n=14, then =7.5, so the median is the average of the 7th and 8th value.

Mode

4. What is the mode of the data?

Mode

Example 2: Finding Centers of Data

- the most frequently occurring number in a data set

5. Describe the distribution of the data.

- the most frequently occurring data value

Data Distribution

Positively Skewed

Distribution

Negatively Skewed

Distribution

Symmetrical

Distribution

Data in Frequency Tables

In frequency tables, the mean =

Categorical Variables

describe

a quality or characteristic. It can be divided into categories. (DUH!)

x

f

fx

This is telling us that "6" appeared in the data 14 times, so to help find the sum, we multiply 6 by 14 and add it to the other total values.

Eg. 'Getting to school.' Categories could be tram, metro, car, teleportation, etc.

Median in Frequency Tables

Quick Check:

Categorical vs. Quantitative

Variables

Categorical!

Quantitative!

1. Vote choice in an election

Quantitative Variables

always have a numerical value.

Quantitative!

2. Time taken in the shower

Categorical!

3. Number of KFC lunches

per week

Quantitative!

4. Favorite candy

Eg. Time spent brushing teeth.

Quantitative!

n+1

5. Killcount in Call of Duty

40+1

=

6. Cost of a new computer in

various stores

Categorical!

2

= 20.5

7. Brands of football shoes

2

So, the median is the average of the 20th and 21st data values. The 20th is 6, and the 21st is 6. So the median is 6.

!

data can be counted.

Discrete

Eg. Test scores, number of pets, etc.

data must be

measured.

Continuous

One Variable Statistics

Eg. Height, weight, time,

etc.

Grade 9 IGCSE Math Extended

So, the mean =

=

sample

This is why we usually take a , which is a collection of data about a small part of the population only. This is obviously easier, and if you take a big enough sample, can

give a good idea about the whole

population.

census

A is collecting data about every individual in an entire population. This is hard to do.

2

n

n-1

If there are data values, the median is the

th data value.

2

continuous

Quantitative variables can

be or .

discrete

14+1

2

Statistics

is the art of solving problems by collecting and analyzing data.

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