STATISTICS (ANALYSIS) : mean, mode & median

The Next Phase in Statistics is Data Analysis. In this segment we will be focusing on the following:

.1 Averages

.2 Histogram

.3 Other forms of presentation (Dot Diagram, Stem and Leaf)

Follow through the following series of tasks

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.1 Averages

'Before you can begin to understand statistics, there are four terms you will need to fully understand. The first term 'average' is something we have been familiar with from a

very early age when we start analyzing our marks on report cards. We add together all of our test results and then divide it by the sum of the total number of marks there are. We often call it the average. However, statistically it's the Mean!' [source: http://math.about.com]

Your task:

1. Define the following statistical terms: Mean, Mode and Median
2. You may refer to the following link for assistance [click here]
3. Provide an example on each of the terms
4. When do we use mean, mode or median?

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.2 Frequency Table and Histogram

Identify the characteristics of a Histogram.

What is/are the primary difference/s between Histogram and Bar Chart?

Your Task

Do a simple survey in class and complete the following tasks

Complete a Frequency Table

• Use Numbers and Plot a Histogram (label the axes and provide a suitable Title)
• Find the (a) mean, (b) mode and (c) median
• Which of the above averages ie. mean, mode or median you think best represents your findings about your survey? Why?

Group 1: Birth months of all your classmates

Group 2: Home location of all your classmates (North, South, East, West)

Group 3: Number of siblings of individual student

Group 4: Types of CCA

Group 5: Favourite genre of movies: Horror, Comedy, Thriller, etc etc

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Other types of Representation

Dot Diagram

Stem and Leaf

Task completed

the following is the work completed by the various groups:

Data is based on class Birthdates

The mean =

The mode =

The median =

Pie charts and frequency diagrams

The following website shows the representation of data as Pie Chart and Frequency diagrams.

Go through the tutorial in the website and complete the given worksheet in class.

Please click here for access to site.

source: http://www.bbc.co.uk/schools/gcsebitesize/maths

STATISTICS (reading)

“We are just statistics, born to consume resources” - Horace (65-8 BC Epistles Book 1)

When information for a statistical investigation is collected and recorded this is referred to as data.

What is a statistical investigation?

There are four processes involved in a statistical investigation

1 Collection of data (information)

Data for a statistical investigation can be collected from records, from surveys, by direct observation or by measuring or counting. Data can be collected for the whole population, which generally means all the people of things that the conclusions of a statistical investigation would apply to, or for a sample of the population.

Collection of data is the first and most important task in an investigation because unless the correct data is collected valid conclusions cannot be made.

2 Organisation and Display of Data

This involves organizing data into tables and/or displaying the data with a suitable graph so that some of the features of the data are more visible.

For the two types of data that we study in detail (categorical and numerical) there are appropriate tables and graphs.

Discrete data can be displayed by:

· Pictogram - display of information using pictures to represent frequency.

· Bar chart – display of information using bars of different lengths to represent the frequency.

This is useful for making comparison over a period of time e.g. exam results

· Pie chart – uses a circle to represent data: useful to show proportions

· Leaf-and-stem diagram – shows all the original data and therefore useful to show trend of data

· Dot diagram – each dot corresponds to one score. The frequency of a number is the number of times it occurs.

· Line graphs

A histogram may be used to display non-discrete (continuous) data

3 Calculation of Descriptive Statistics

There are some statistics that are universally used to describe a set of data.

Calculating statistics that indicate the centre of the data and the spread of the data give us a picture of the sample or population under investigation.

Reading : http://www.mste.uiuc.edu/hill/dstat/dstat.html

4 Interpretation of Statistical Data

This process involves explaining the meaning of the table, graph or descriptive statistics in terms of the variable or theory to be investigated.

Some questions that you may ask to interpret statistical data:

1. What is the title of the chart, table or graph?

2. What is the purpose of this chart, table or graph?

3. What do the labels/headings tell you?

4. What key information does the data provide?

5. What is your main conclusion about the data?

6. How were you able to interpret this chart, table or graph?

7. Who created the chart, table or graph?

8. What information does the chart, table or graph add to the given account(s) of event?

9. Does the information in this chart, table or graph support or contradict information

that you have read about this event?

Types of data

Data are individual observations of a variable. A variable is a quantity that can have a value recorded for it or to which we can assign an attribute or quality.

There are two types of variable that we commonly deal with :

Categorical variables

A quality is recorded for this type of variable.

The information collected is called categorical data.

Examples of categorical variables are:

• Colour of eyes : the categories would be blue, brown, hazel, green, violet
• Gender : Male or Female
• Marital Status : Single, Married, Separated, Divorced

Numerical variables

A numerical value is recorded for this type of variable. The information collected is called numerical data.

Examples of numerical variables are :

• The number of people in a household : the variable could take the values 1, 2, 3, 4, …

• The weight of new born babies : the variable could take any value on the number line but it is likely to be in the range of 0.5 kg to 8 kg.

• The score out of 30 on a test : the variable could take the values 0, 1, 2, …, 30

Chap 16 Data Handling (Lesson 1) Worksheet 16.1 Q2

The Pie Chart below represents the traffic condition outside SST at 7.25 am on a typical morning.

(a) Find the angle of the sector representing motorcycle to the nearest degree.

(b) Find the percentage of sector representing cars, correct your answer to 3 significant figures.

courtesy of Ms LohKY

Chap 16 Data Handling (Lesson 1) Worksheet 16.1 Q1

The bar chart above shows the traffic condition outside SST at 7.05 in a typical morning.

(a) Find the number of heavy vehicles observed at 7.05 am

(b) How many more cars are there as compared to heavy vehicles at 7.05 am?

(c) What is the total number of vehicles on the road at 7.05 am?