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ISDS-361AExercises 1. Mean, Median, Mode, Range, Variance & SD Panayiotis Skordi

1. A basketball player has the following points for seven games:

20, 25, 32, 18, 19, 22, 30

Compute the following measures of central location:
a. mean
b. median
c. mode

Answers

a. Mean[pic]

b. Median[pic]

c. Mode There is no mode.

2. Consider the following population of measurements:

162, 152, 177, 157, 184, 176, 165, 181, 170, 163

a. compute the mean
b. compute the median

Answers

a. Mean[pic]

b. Median

[pic]

[pic]

3. The following data represent the number of children in a sample of 10 families from a certain community:

4, 2, 1, 1, 5, 3, 0, 1, 0, 2

a. compute the range
b. compute the variance
c. compute the standard deviation

Answers

a. Range [pic]

b. Variance[pic]

Remember that [pic]

[pic][pic][pic][pic]

14 2.14.41
22 0.10.01
31-0.90.81
41-0.90.81
55 3.19.61
63 1.11.21
70-1.93.61
81-0.90.81
90-1.93.61
102 0.10.01

Total1924.9

[pic]

Method 2[pic]

[pic][pic][pic]
1416
224
311
411
5525
639
700
811
900
1024

Total1961

[pic]

This is the same answer – as we would expect.

c. The standard deviation is [pic]

4. Consider the following population of measurements:

162, 152, 177, 157, 184, 176, 165, 181, 170, 163

a. compute the standard deviation

Answer

[pic]

Remember that [pic]

[pic][pic][pic][pic]

|1 |162 | |-6.70 | |44.89 | |2 |152 | |-16.70 | |278.89 | |3 |177 | |8.30 | |68.89 | |4 |157 | |-11.70 | |136.89 | |5 |184 | |15.30 | |234.09 | |6 |176 | |7.30 | |53.29 | |7 |165 | |-3.70 | |13.69 | |8 |181 | |12.30 | |151.29 | |9 |170 | |1.30 | |1.69 | |10 |163 | |-5.70 | |32.49 | | | | | | | | | | | | | | | |Total |1687.0 | | | |1016.10 |

[pic]

The standard deviation is the square root of the variance

[pic]

Method 2[pic]

[pic][pic][pic]

|1 |162 | |26244 |
|2 |152 | |23104 |
|3 |177 | |31329 |
|4 |157 | |24649 |
|5 |184 | |33856 |
|6 |176 | |30976 |
|7 |165 | |27225 |
|8 |181 | |32761 |
|9 |170 | |28900 |
|10 |163 | |26569 |
| | | | |
| | | | |
| |1687 | |285613 |

[pic]

As before, the standard deviation is the square root of the variance

[pic]

5. Monthly rent data...
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