Question

Millions of Americans work from offices in their homes. Following is a sample of age data for individuals who work at home.

18     54     20     46     25     48    53     27

40    36     42     25    27   33     28

1. Compute the mean, median and mode?

2. The median age of the population of all adults is 36 years (The World Almanac, 2006)

Use the median age of the preceding data to comment on whether the at-home workers tend to be younger or older than the population of all adults

3. Compute the sample variance and sample standard deviation.

Answer 1

1. Mean = sum of all observations/no of observations = sum/ 15 = 34.8

Median

Arrange the data in ascending order : 18,20,25,25,27,27,28,33,36,40,42,46,48, 53,54

Going by this order 8th number will be median i.e 33

Mode : Number that occurs maximum number of times i.e 25 and 27

2. SInce 36 is more than 33 , therefor median age of at-homw workers is more, hence, they are older.

3. Variance :sum of x minus the mean squared divided by n, where x is observation

In this case, variance = 129.63

Standard deviation : square root of variance = 11.39