A researcher has obtained the number of hours worked per wee

A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students. Please make sure you must use the manual procedure explained in your textbook in chapter 3. You should also show mathematical steps in detail. Your answer will be marked down by 50% if you just include the final answer.(20 points) 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20 a. Calculate mean, range, and standard deviation. b. Calculate 40th percentile and median.

Solution

Observations : 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20

Mean = Sum of all observations/No. of observations = (40 + 25+ 35......+20)/15 = 375/15 = 25

range = Maximum - Minimum = 40 - 5 = 35

standard deviation = sqrt(sum(x(i) - mean)²) / n-1)

= sqrt(1800/14)

= 11.3389

Arranging the observations in ascending order

5 10 10 20 20 20 20 25 30 30 30 35 40 40 40

Median = midllemost observation = 25

40% percentile = 20

(60% of the observations are more than 20)