Question

According to the National Education Association (NEA), teachers generally spend more than 40 hours each week working on instructional duties (NEA website, April 2012). The following data show the number of hours worked per week for a sample of 13 high school science teachers and a sample of 11 high school English teachers. High School Science Teachers: 53 56 54 54 55 58 49 61 54 54 52 53 54 High School English Teachers: 52 47 50 46 47 48 49 46 55 44 47

a. What is the median number of hours worked per week for the sample of 13 high
b. What is the median number of hours worked per week for the sample of 11 high
c. Which group has the higher median number of hours worked per week? What is the school science teachers? school English teachers? difference between the median number of hours worked per week?

Answer 1

(a) The median number of hours worked per week for a sample of 13 high school science teachers is 54.

(b) The median number of hours worked per week for a sample of 11 high school English teachers is 47.

(c) High School Science Teachers has the higher median number of hours worked per week.

Explanation:

We are given the data below which shows the number of hours worked per week for a sample of 13 high school science teachers and a sample of 11 high school English teachers.

High School Science Teachers: 49, 52, 53, 53, 54, 54, 54, 54, 54, 55, 56, 58, 61,

High School English Teachers: 44, 46, 46, 47, 47, 47, 48, 49, 50, 52, 55

The above data is arranged in ascending order also.

Now, for calculating median we have to first observe that the number of observations (n) in our data is even or odd, i.e;

• If n is odd, then the formula for calculating median is given by;

Median =
`((n+1)/(2))^(th) \text{ obs.}`

• If n is even, then the formula for calculating median is given by;

Median =
`\frac{((n)/(2))^(th)\text{ obs.} +((n)/(2)+1)^(th)\text{ obs.} }{2}`

(a) In the High school science teachers' data, the number of observations is odd, i.e. n = 13.

So, Median =
`((n+1)/(2))^(th) \text{ obs.}`

=
`((13+1)/(2))^(th) \text{ obs.}`

=
`((14)/(2))^(th) \text{ obs.}`

=
`7^(th) \text{ obs.}` = 54

Hence, the median number of hours worked per week for a sample of 13 high school science teachers is 54.

(b) In the High school English teachers' data, the number of observations is odd, i.e. n = 11.

So, Median =
`((n+1)/(2))^(th) \text{ obs.}`

=
`((11+1)/(2))^(th) \text{ obs.}`

=
`((12)/(2))^(th) \text{ obs.}`

=
`6^(th) \text{ obs.}` = 47

Hence, the median number of hours worked per week for a sample of 11 high school English teachers is 47.

(c) As we can see above that High School Science Teachers has the higher median number of hours worked per week as 54 > 47.

The difference between the median number of hours worked per week for both high school teachers = 54 - 47 = 7 hours.