Describe the measures of dispersion and explain why standard ...

[Destiiny22]

Describe the measures of dispersion and explain why standard deviation is used most often.

Question 2

A perceptual map shows perceived strengths of a firm (compared to its competitors) from the customers' perspective.
 a. True
  b. False
 Indicate whether the statement is true or false

[upturnedfurball]

Answer to Question 1

There are several measures of dispersion:
(1) Range: the simplest measure and is the distance between the smallest and the largest value of a frequency distribution.
(2) Deviation scores: measures how far any observation is from the mean. Average deviation is derived by calculating the deviation score of each observation value, summing these scores, and then dividing by the sample size. However, positive deviation scores are canceled out by negative scores, leaving an average deviation value of zero no matter how wide the spread.
(3) Variance: a means of eliminating the sign problem caused by the negative deviations canceling out the positive deviations is to square the deviation scores. It's a good index of dispersion and will grow larger as the observations tend to differ increasingly from one another and from the mean. However, it reflects a unit of measurement that has been squared.
(3) Standard deviation: the most valuable index of spread, or dispersion. It is the square root of the variance for a distribution, which eliminates the drawback of having the measure of dispersion in squared units rather than in the original measurement units.

Answer to Question 2

True