In the Venn Diagram you will compare and contrast the definitions and meanings o

Question

In the Venn Diagram you will compare and contrast the definitions and meanings of three measures of variability. They are a) Range, b) Variance, and c) Standard Deviation. For those of you who are more visual, I have included the Expanded Venn Diagram. You are to push for 4 to 5 ideas for each section. Some of the ideas will come from the textbook and material covered in the powerpoints. Some other ideas will be inferred from what you read. Do not copy the information from the text or powerpoint slides. Try to use your own words as much as possible so that I can see that you fully understand the three concepts. .Please use the accompanying answer template to type your answers 1. 4 2. 7 5. 3. 1. 2. 3. 4. 5. 6. 7. Unique to the concept of range Unique to the concept of variance Unique to the concept of standard deviation Similarities between range and variance Similarities between range and standard deviation Similarities between variance and standard deviation Similarities among all the three concepts-range, variance, and standard deviation

Explanation / Answer

Dear student please draw 3 large intersecting circles (large enough so that you can write the points inside it ) and write the points accordingly.

1. Range is defined as the difference between the largest and lowest values in a data set.

2. Variance measures how far a data set is spread out from the mean. Variance is defined as the average of the squared difference of the observations from the mean .

3. Standard deviation is defined as the square root of the variance. Standard deviation is defined as the square root of the average of the squared difference of the observations from the mean.

4. Both of range and variance are measures of dispersion of a data set and they measures the spreadness of the data set.

5. Both of range and standard deviation are measures of dispersion of a data set and they measures the spreadness of the data set.

6. Both of variance and standard deviation are measures of dispersion of a data set. standard deviation is the square root of variance.

7. range ,variance and standard deviation are three measures of dispersion in a data set and each of them measures the scatterness or spreadness of the data set.

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