1. Unit 3 – One Variable Statistics
Common Distributions
Unit 3 – One Variable Statistics

2. Distribution and Properties
Distribution – The way in which something is shared out among a group or spread over an area.
Symmetric - The same on both sides
Skewed – a higher number of values on one side (not symmetric/asymmetric)
Uniform – The same for all.

3. Classify State if the distributions are symmetric, skewed or uniform
not skewed
not uniform
Not Skewed
Not uniform
Symmetric
not skewed
Uniform
Asymmetric
Skewed
Not uniform

4. Distributions Symmetric can be: Normal Bimodal Uniform
Asymmetric are skewed right or left

5. Normal Distribution
Example 1 – A pair of dice was rolled 75 times and the sum recorded.
Commonly referred to as “bell-curves” or “mound-shaped” distributions
The middle interval(s) will have the greatest frequency (i.e. the tallest bar)
All other intervals will have decreasing frequencies as you move away from the centre of the graph (i.e. the bars get smaller as you move out to the edges)

6. Bimodal Distribution
Example 2: A class of grade 6 and grade 1 students each measured their heights. They recorded and graphed them.
Look like inverted normal distributions
The intervals with the highest frequencies (the tallest bars) are at either end of the graph, and the interval with the lowest frequency is in the centre.
Frequencies increase as you move away from the centre of the graph.

7. Uniform Distribution
Example 3: A die is rolled 50 times. The face is recorded and graphed.
The frequencies of each interval are approximately equal.

8. Is the tail on the left or right of the picture?
That’s the tail
It’s on the right
It’s on the left

9. Skewed Distributions
Tail – The tail of a distribution is the side with the lowest frequencies.
Right-Skewed Graphs – the bars with the highest frequencies are on the left side and the frequencies decrease as you move right.
Left-Skewed Graphs – the bars with the highest frequencies are on the right side and the frequencies decrease as you move left.

10. Left-Skewed Distribution
Even though there is a low-frequency bar on the right side in this example, the trend is still left-skewed.