Question

For the Following data: 5, 15, 18, 10, 8, 12, 16, 10, and 6 Find:

a) Q1 = 25%; Q2= 50%; Q3 = 75%. Quartile and IQR= Inter Quartile Range

b) Box Plot Figure with Upper & Lower Limit, Whiskers and Outlier(s) if any

PLEASE SHOW DETAIL OF YOUR SET UP, FORMULA, CALCULATION. PLEASE NO EXCEL! Thank you!

Answer 1

First we sort the data in ascending order as below

5
6
8
10
10
12
15
16
18

a) First we find the median (Q2=50%)

Let n be the number of observations

If n is odd then the median is (n+1)/2 th observation. If n is even then median is the average of n/2 th and (n/2+1)th observations

Here n=9. Hence the median in (n+1/2 = (9+1)/2 = 5th observation, which is 10

The first quartile or Q1 is the observation with 25% of observations are less than this observation.

Tukey's method of getting this is as below

Q1 is the median of the data less than or equal to the median.

The less than median, including the median is

5

6

8

10

10

There are 5 observations. Hence the median of this is (5+1)/2= 3rd observation, ehich is 8

Q3 or the third quartile is the observation with 75% of the observations are less than this value

Q3 is the median of the data which is equal to or more than the median. The data is

10

12

15

16

18

Since there are 5 observations, the median of this set is (5+1)/2 = 3rd observation which is 15

IQR or the inter quartile range is

b) We calculate the following

Minimum value :of this data set is 5

Maximum value of this data set is 18

The lower value of the fence is

The upper value of the fence is

Any value which is less than -2.5 and more than 25.5 is an outlier. In this dataset we do not have any outlier

Now the box plot