Question

The mean and the median are two types of measures of center. 1. Give a detailed real-world example of when the median is preferred over the mean. Explain why the median is a preferred measure in your example. Refer to the eText and resources in the course Materials folder. 2. Create a number collection, any 7-12 numbers of your choice. Arrange them in order and find Median and Mean. Calculate Sample Variance and Standard Deviation for your sample To find Variance and Standard Deviation on Excel: One way sample variance and sample standard deviation can be calculated on Excel: Open a spreadsheet. enter data in first column. Lets say data is 3,6,8,12,16,17,20,23,24. It would be entered in cells A1 to A9. Go to Formulas at top ribbon, More Functions, Statistical, Scroll to var.s for sample variance. In No.1 dialog box enter cell range A1:A9. Note the variance value appears in bottom right of dialog box. (56.75) Repeat to find standard deviation. Scroll to stdev.s for sample standard deviation. (7.533).

Answer 1

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1. Mean is the average of all data values, thus considers all the values and is affected by the extreme values. Mean tends to shift towards higher number. As far as median is concerned it is positional average of the data which also consider all the data values but are not affected by the extreme values.

We generally prefer median over mean where the data is skewed. i.e. not normal.

Real example : Where we have diverse group of observations we will prefer median as presence of extreme values will be there.

In mumbai , India earning gap is very huge with Range = 5$ to 100 million $, so mean earning would not be the right measure as few people earning huge amount of money will distort the average. Median is preferable.

b). Below is the set of 10 values randomly chosen.

4
6
3
13
15
8
9
11
14
19

Sorted data
3
4
6
8
9
11
13
14
15
19

Mean = Summation (X's/no. of data values) = 10.2

Median = 10

sample standard deviation = 5.138 (Using STDEV.S function in excel)

Sample variance = 26.4 (Using VAR.S function in excel)