Download Often you want to find the probability that a variable falls in a

MDM 4U1
Unit #6 Continous Probability Distributions
Date:__________________
8.1 Continuous Probability Distributions
Distributions that we examined in chapter 7 deal with discrete data and therefore gave rise to discrete
distributions. For example: counting the number of outcomes for drawing a card or tossing three coins.
However, many characteristics of a population such as height, measuring time taken to complete a task or
the maximum distance a ball cam be thrown are continuous in nature and have fractional or decimal values.
Just as with discrete data, however, these continuous variables have statistical distributions. Continuous
probability distributions allow fractional values and can be graphed as smooth curves.
Example 1:
Identify each of the following situations as discrete distributions or continuous distributions.
a) counting the number of outcomes for drawing a card
b) measuring the time taken to complete a task
c) counting the number of outcomes when tossing three coins
d) measuring the maximum distance a ball can be thrown
Continuous Data Histograms
A distribution which is not symmetric may be positively skewed (tail pulled to the right) or negatively skewed (tail
pulled to the left).
Type:_____________________________
Example:___________________________
____________________________
___________________________
MDM 4U1
Type:_______________________________
_______________________________
Example:_____________________________
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Classification of Histograms
Using the following data sets calculate the mean, median, mode, and standard deviation. Graph each data
set on the grids provided. Label the shape of each graph. Compare your graphs to your measures of central
tendency and summarize your findings.
Example: Age of cousins {12, 15, 8, 12, 15, 10, 3, 14, 15}
Frequency
Age of Cousins
3.5
3
2.5
2
1.5
1
0.5
0
3.5-5.5 5.5-7.5 7.5-9.5
9.511.5
Age (years)
From Excel:
Mean : 11.6
Mode: 12
Median: 15
Standard Deviation: 4.03
Shape:______________________
Summary:
11.513.5
13.515.5
MDM 4U1
Distribution of Data
We can use a spreadsheet program to create frequency histograms (recall chapter 2!!!) for the
following groups of data taken from a variety of real life situations. We draw a smooth, continuous
curve representing the general shape of the distribution.
Example:
Spider Solitaire
400-449 450-499 500-549 550-599 600-659 650-699 700-749 750-799 800-849
Score
10
6
4
0
4
6
10
15
Frequency 15
Spider Solitaire Score Frequency
Histogram
16
14
Frequency
12
Shape:____________________
10
8
6
4
2
0
400- 450- 500- 550- 600- 650- 700- 750- 800449 499 549 599 659 699 749 799 849
Score
Often you want to find the probability that a variable falls in a particular range of values. This kind of
probability can be determined from the area under the probability curve. The curve itself represents the
probability distribution, the probability per unit of the continuous variable.
*Theoretical probability for a continuous random variable is determined over a range of values
(i.e. the probability that the score of a spider solitae game is 450 – 499)
*The probability that a continuous random variable) takes any single value is ZERO
Many distribution curves can be modelled with equations that allow the areas to be calculated rather
than estimated. The most commonly used one is the normal distribution which we will discover next
day.
Homework - pg.419 #2[identify the type of distribution]
#3,4 both questions use Excel
 create a frequency histogram and draw a smooth continuous curve
 describe the shape of the distribution and give reasons
 calculate mean, median, mode and standard deviation and
summarize how it relates to your description of the distribution.
#5