stat Measures of Variation 1.The measures of variation measure the _____________

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stat

Measures of Variation

1.The measures of variation measure the ______________in the data.

2.Give an example of two sets of data with the same mean but different variance or standard deviation.

3.Give an example of a data set that has a zero standard deviation.

4. What is the range? What is one biggest disadvantage in using the range to measure the spread in the data?

5. Write the symbol and the formula for each of the following:

a) Sample mean (      )=                                   b)Population mean (      )=

c)Sample Variance (       ) =                              d)Sample Standard Deviation (       )=

e) Population Variance (      ) =                           e) Population Standard Deviation (       )=

6. Standard deviation is the _________________________________ of the variance.

7. List important properties of Standard deviation

8. Write the formula for the Coefficient of Variation (CV)

9. Give an example of a question that can be answered with CV ?

9. If a coefficient of variation for a particular population is 4.7 and for another population it is 12.6, what can you conclude about the variations in the two populations?

10) State the Empirical Rule in your own words

11)Define the z-score

13)Write the formula for z-score

14)Explain how the z-score is used to identify significantly high or significantly low values

Explanation / Answer

(According to Chegg policy, only four subquestions will be answered. Please post the remaining in another question)

1.The measures of variation measure the _______spread_______in the data.

2.Give an example of two sets of data with the same mean but different variance or standard deviation.

Set 1: -2, -1, 0, 1, 2

Mean is 0.

Variance is (4 + 1 + 0 + 1 + 4)/5 = 10 / 5 = 2

Set 2: -3, 0, 3

Mean is again 0.

Variance is (9 + 0 + 9) / 3 = 6.

3.Give an example of a data set that has a zero standard deviation.

The data set 5,5,5,5,5,5,5,5 or in general any set where every value is the same has zero standard deviation.

4. What is the range? What is one biggest disadvantage in using the range to measure the spread in the data?

The range is the difference between maximum and minimum values of a data set. The biggest disadvantage of range is that it does not measure the spread of the majority of values in a data set—it only measures the spread between maximum and minimum values.

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