Question

1. The following data is the annual income (in $1,000s of U.S. dollars) taken from nine randomly chosen students in an MPH program: 37 102 34 12 111 56 72 17 33

1. Calculate the sample mean income
2. Calculate the sample median income
3. Calculate the sample standard deviation of these incomes
4. What population could this sample represent?
5. Which would change by a larger amount—the mean or median—if the 34 were replaced by 17, and the 12 replaced by a 31?

Answer 1

a. Sample mean income:

To find the sample mean we have to find the average of all the data in the sample

Sample mean =( 37+102+34+12+111+56+72+17+33)/9 = 52.67

Sample mean of income is 52.67(in $1000s of U.S dollars)

b. Sample median income:

To find the sample median we 1st arrange the sample data in ascending order

After arranging the data: 12,17,33,34,37,56,72,102,111

to find the median here we find the ((n+1)/2) th term of the arranged data

here n= 9 (number of data)

so we have to find ((9+1)/2)th term = 5th term

sample median is 5th term which is 37

Sample median income is 37(in $1000s of U.S dollars)

c. Sample standard deviation

let Xi represent the sample data

let be the sample mean income

formula:

applying the formula we get 35.58

Sample standard deviation of these income is 35.58

d. This sample could represent the population of 'Annual income of of students in MPH program'

e. If the 34 were replaced by 17, and the 12 replaced by a 31 in sample data then

mean= 52.89 (done in same way as a. only replacing the said number)

median = 37 (done in same way as b. only replacing the said number)

So the median remained the same while mean changed a little bit

Answer: mean would change by a large amount than median