Question

Find the median, first quartile (Q1) and the third quartile (Q3) for the data shown, which is already sorted. The number of data is n= 10.

Kate Kozak's algorithm:

Sort the data and compute the median.

When n is an odd number, the median is the center value.

When n is an even number, the median is the center value.

After computing the median, Q1 is the median of the 1st half of the data, not including the median value.

Q3 is the median of the 2nd half of the data, not including the median value.

Do not round your answers.

x

2.8

5.7

9.6

17.9

19.8

21.4

23

23.1

26.6

27.7

Q1 =
Q3 =

Answer 1

The given sample data is sorted as:

2.8
5.7
9.6
17.9
19.8
21.4
23
23.1
26.6
27.7

a) Median:

The median is calculated as the middle value of the sorted data set since the sample size is 10 hence the middle value is between 5th and 6th value hence the median is (19.8+21.4)/2=20.6

b) Q1 is the first quartile value which is the median value of the first half, the middle value of the first half is the 3rd value which is 9.6

c) Q3 is the 3rd quartile which is the middle value of the 2nd half of the data set hence the Q3 is the 8th value which is 23.1