Question

Compute Median, Q1, Q3, and IQR for the following data below

Given: 10, 20, 12, 17, and 16

**Provide interpretation of your calculations**

Answer 1

Median -

To find the median, we arrange the given series in ascending order i.e. from smallest to largest value. If there is an odd number in series, the median is the middle value. If there is even numbers in series, the median is the average of the two middle values Median can also be called as Q2.

Ascending order is -

10

12

16

17

20

Median is th middle value i.e. 16 because there is odd numbers in given series,

Q1 - first quartile

Q1 is the median of the lower half of the data set. Data set is divided in 2 parts by Median i.e. Q2. If there is an odd number in Lower half of series, the Q1 is the middle value. If there is even numbers in Lower half of series, the Q1 is the average of the two middle values.

In the given series lower half is

10

12

16

Q1 is th middle value i.e. 12 because there is odd numbers in Lower half of given series,

Q3 - third quartile

Q3 is the median of the upper half of the data set. Data set is divided in 2 parts by Median i.e. Q2. If there is an odd number in upper half of series, the Q3 is the middle value. If there is even numbers in upper half of series, the Q3 is the average of the two middle values.

In the given series upper half is-

16

17

20

Q3 is th middle value i.e. 17 because there is odd numbers in upper half of given series,

IQR - Interquartile range

The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. The interquartile range is equal to Q3 minus Q1.

Q1 is the middle value in the first half of the data set. Since there are an odd number of data points in the first half of the data set, the middle value is, Q1 = 12. Q3 is the middle value in the second half of the data set. Again, since the second half of the data set has an odd number of observations, the middle value is is, Q3 = 17. The interquartile range is Q3 minus Q1,

so IQR = 17- 12 = 5.

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