Statistics is the collecting, the grouping, and understanding of data.

Data is the raw facts and figures that would be collected, for example, the number of children in a home, the heights of children in a class or the number of people in an office who wear glasses.

Data can take on take on two forms discrete or continuous.

Discrete data is data that can take on exact values, for example, the number of cars passing a checkpoint in 30 minutes or the number of tomatoes on each plant or the number of children in a home.

There cannot be 2 1/2 children in a home because you cannot have 1/2 of a child but you can have 2 children living in a home or 46 cars passing a checkpoint in 30 minutes or 6 tomatoes on each plant.

In this example 2, 46 and 6 are examples of exact data or discrete data and may be described as the number of times a situation may occur. The number of times a situation may occur is called the frequency.

Continuous data is data that cannot take exact values, for example, the speeds of vehicles, the weights of flour or the time taken for a class to complete a task.

Therefore, the speed, the weight or time can take on a large range of values. For example, the speed of a car can be 2.35 miles per hour, the weight of flour 6 1/2 pounds, or a class may take 1/2 of an hour to complete a task.

Tables and graphs are used to organize and arrange data so that it is more easily understood by the viewer.

Data is first collected and organised, using a tally table or chart, and then displayed using one of many types of graphs. Tables and graphs, therefore, go hand in hand since the information used in tables is frequently also used for the basis of graphs.

There are many types graphs that can be used to display data. There are Pictographs, Bar Graphs or Column Graphs, and Pie or Circle Charts.

Tally tables are one of the most fundamental of tables used in Statistics to organise and arrange data in a way that would be helpful in understanding the data being analysed. Tally tables are used to analyse a small number of discrete data.

If we were to analyse the ways in which children in a class got to school, we can use a tally table to represent this.

For example, if we know that 9 children walk to school, 3 ride a bike, 6 ride in a car and 12 caught the bus this information can be displayed in a tally table.

For every one score a vertical line, |, is used. The number four would therefore would be represented like this, ||||.
When the number is five, a slanted stroke, , is placed through the four stokes looking like this,

Before we talk about graphs it is important for us to know how to draw and label a graph. A graph normally consists of a an x-axis which is represented by a horizontal line and a y-axis which is represented by a vertical line.

Next, marks must be placed on your X and Y axes that will tell you where to place your data. Then , it is equally important to label both axes, that is, give them both a name that describes the nature of its values.

For example, if we analysed the different ways children in a class may get to school then on the x-axis we can label it "Method".

The different methods children use to get to school are walking, catching the bus, riding in a car or on a bicycle, taking a train or a taxi, etc.

The y-axis can be labelled then "Number of Children" to represent the number of children who may take a certain method of transportation. This line, in our example, increases in multiples of 2.

Finally, the entire graph can be labelled "Getting to School" because it describes the different ways in which children get to school.

A pictograph is a pictorial representation of numerical data that uses cartoon or simple drawings to depict quantities. It makes comparisons easily understandable and is excellent for young audiences.

In this example it can be seen that there are clearly 5 apples, 6 oranges and 6 bunches of grapes.

A bar graph is a graph which visually displays amounts or frequencies of different characteristics of data. For example, the favourite after school activities include visit with friends, talk on phone, play sports, earn money, use computers.

The frequency or number of students that visit with friends are 175, the number that talk on the phone are 168, the number that play sports are 120, the number that earn money are 120 and the number that use computers are 65. This information can be displayed clearly using the table and the bar graph below.

The mean, median and mode are really useful ways of comparing sets of data.

Mean

The mean is the average of a set of data. The mean is calculated by adding up all the numbers and then dividing it by the number of numbers.

For example, 4 tests results are 15, 18, 22, 20. The sum is: 75. If we divide 75 by 4 we will get 18.75. Therefore, the mean of 15, 18, 22 and 20 is 18.75.

Mode

The mode is the score that appears the most in a given set of data. To figure it out, all have to do is determine the score or number that appeared the most.

For example, the data given is 10, 12, 12, 10, 9, 11, 11, 13, 11, 9, 8. If we placed it in numerical order then we can see clearly the number that occurs the most.

8, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13

We can see that the number 11 occurs the most. Therefore, the mode is 11.

Median

The median is the middle score of a set of data arranged in a numerical order

To calculate the median we must first arrange the data in numerical order either ascending or descending. Then, we must determine the middle number.

There are two situations that we face when finding the median. Those two situations are:

1. when the number of numbers are odd and

2. when the number of numbers are even.

Odd Number of Numbers

For example, find the median of: 9, 3, 44, 17, 15

3, 9, 15, 17, 44 (ascending order)

The Median is: 15

Even Number of Numbers

For example, find the median of: 8, 3, 44, 17, 12, 6

3, 6, 8, 12, 17, 44 (ascending order)

Add the 2 middles numbers and divide by 2:

8 + 12 = 20 / 2 = 10

The Median is 10.