STAT 245 Lecture Notes - Lecture 2: 5,6,7,8, Histogram, Bar Chart
Stat 245 Lecture 2 – Distributions and Graphs
A survey was done to determine the eye colour of a sample of 50 students. The results are as follow:
What do we see from the above result? All we can tell is that there are students who have hazel eyes,
brown eyes, green eyes, blue eyes, etc. The above presentation is just a clutter of eye colour.
Just as our bedrooms can be filled with nothing but clutter, we need to organise this clutter so that we
can make some sense of the data we just collected. So we need to organise our data, just like we need to
organise the things in our bedrooms.
Organising Data into a Distribution
A distribution summarises the organisation of raw data into
What values each variable takes, and
How often each value occurs (i.e. the frequency of each value).
We can summarise the results of the eye colours of students into a Frequency Distribution as follows:
Definitions
1. Frequency – The number of times a value occurs for a variable.
Example: Frequency of students with blue eyes in the sample = 13.
2. Relative frequency
Example: Relative frequency of students in the sample with blue eyes
Charts
A picture paints a thousand words, so a chart depicts the frequency distribution in a very nice way. There
are many different types of charts:
1. Bar Graph
Rectangles of equal width with heights / lengths equal to the category’s frequency or relative
frequency or percentage of occurrence.
In a bar graph, bars do NOT touch each other.
Example:
2. Histogram
Similar to the bar graph, rectangles of equal width with heights / lengths equal to the category’s
frequency or relative frequency or percentage of occurrence.
In a histogram, bars touch each other.
Example:
3. Pie Charts
Each slice of the pie is proportional to the relative frequency or percentage of the category it
represents.
Examples:
Document Summary
Stat 245 lecture 2 distributions and graphs. A survey was done to determine the eye colour of a sample of 50 students. All we can tell is that there are students who have hazel eyes, brown eyes, green eyes, blue eyes, etc. The above presentation is just a clutter of eye colour. Just as our bedrooms can be filled with nothing but clutter, we need to organise this clutter so that we can make some sense of the data we just collected. So we need to organise our data, just like we need to organise the things in our bedrooms. A distribution summarises the organisation of raw data into. How often each value occurs (i. e. the frequency of each value). We can summarise the results of the eye colours of students into a frequency distribution as follows: Frequency the number of times a value occurs for a variable. Example: frequency of students with blue eyes in the sample = 13.
