Measures of Variability/Dispersion

Measures of Variability/Dispersion

by: Ph-USA Guru

What you'll be learning today:

• Define Variability or Dispersion.

• Know the importance of measuring variability.

• Calculate the different measures of Variability.

Poll

Are you ready?

• Yes

• No

The Importance of Measuring Variability

(COPY!!!COPY!!!COPY!!!)

• Central tendency - Numbers that describe what is typical or average (central) in a distribution.

• •Measures of Variability - Numbers that describe diversity or variability in the distribution.

• These two types of measures together help us to sum up a distribution of scores without looking at each and every score.

The Importance of Measuring Variability

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• Measures of central tendency tell you about typical (or central) scores.

• Measures of variation reveal how far from the typical or central score that the distribution tends to vary.

MEASURES OF VARIABILITY

• RANGE

• MEAN ABSOLUTE DEVIATION (MAD)

• VARIANCE

• STANDARD DEVIATION

• COEFFICIENT OF VARIATION

Fill in the Blanks

What is the range of the given data? 18, 20, 21, 21, 23, 23?

Open Ended

How did you get the range in the previous question? Give the formula.

Measures of Variability or Dispersion

#1: THE RANGE

THE RANGE

• It is simply the difference between the largest and smallest values in the sample.

• Range is the simplest measure of variability.

• Note that range is highly sensitive to the largest and smallest values. 

Characteristics of the range are:

• Only two values are used in the calculation.

• It is influenced by extreme values.

• It is easy to compute and understand.

• It can be distorted by an extreme values

Suppose a statistics instructor had two classes with ages indicated:

• A.M. Class 18, 20, 21, 21, 23, 23

• P.M. Class 17, 17, 18, 20, 25, 29

• Remember that "a small value for a measure of dispersion indicates that the data are clustered closely around the mean.

• Conversely, a large measure of dispersion indicates that the mean is not reliable and its not representative of the data.

Fill in the Blanks

Find the range of the A.M. Class.

A.M. Class 18, 20, 21, 21, 23, 23

Fill in the Blanks

Find the range of the A.M. Class.

P.M. Class 17, 17, 18, 20, 25, 29

Multiple Choice

Which of the two has more spread? A.M. class or P.M. class?

• A.M. Class

• P.M. Class

REMEMBER!!!

• Remember that "a small value for a measure of dispersion indicates that the data are clustered closely around the mean.

• The smaller the value the better it is.

Multiple Select

Why the range is NOT reliable measure of variability?

• Only two values are used in the calculation.

• It is influenced by extreme values.

Open Ended

Any question/clarification.

#2: MEAN ABSOLUTE DEVIATION

(MAD)

MEAN DEVIATION

(Copy!!!Copy!!!Copy!!!)

• In contrast to the range, the Mean Deviation considers all the data.

• Mean Deviation: The arithmetic mean of the absolute values of the deviations from the arithmetic mean.

MEAN DEVIATION FORMULA

(COPY!!! COPY!!!)

• MD = Mean Deviation

• X = is the value of each observation

•  $\overline{X}$  = is the arithmetic mean

• n = is the total number of sample

• I I = indicates the absolute value

How to find the Mean Absolute Deviation?

• Step 1: Find the mean  $\overline{X}$  

• Step 2: Subtract the mean form each score (X).

• Step 3: Get the absolute value of the difference of the scores and the mean.  $\left|X\ -\ \overline{X}\right|$  

• Step 4: Add the difference of the scores and the mean.  $\Sigma\left|X\ -\ \overline{X}\right|$  

• Use the FORMULA.

Example: Find the Mean Absolute Deviation: 17, 17, 18, 20, 25, 29

• Step 1: Find the mean.

Fill in the Blanks

What is the mean of the data: 17, 17, 18, 20, 25, 29

Fill in the Blanks

Find the Range

58, 62, 85, 87, 91, 9:

Fill in the Blanks

Find the Mean:

58, 62, 85, 87, 91, 99

(Round your answer to whole number)

Open Ended

Find the Mean Absolute Deviation:
58, 62, 85, 87, 91, 99

 $\overline{X}$  = 80

Open Ended

Let me know if you have any question(s). Type here.

Poll

Choose all that applies:

Today,

• I can solve the range and the mean absolute deviation.

• I cannot solve the range and the mean absolute deviation. I need more example.

• I copied the notes today.

• I did not copy the notes today. Need a copy of the lesson.