Unit 1 BP801T median with solved examples

1. MEDIAN?
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 1

2. 1.Median represents the middle value for any group.
2. It is the point at which half the data is more and half the data is less.
3.Median helps to represent a large number of data points with a single data
point.
4. The median is the easiest statistical measure to calculate.
5. For calculation of median, the data has to be arranged in ascending order,
and then the middlemost data point represents the median of the data.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 2

3. 6. Further, the calculation of the median depends on the number of data points.
7. For an odd number of data, the median is the middlemost data, and for an
even number of data, the median is the average of the two middle values.
8. Let us learn more about median, calculation of median for even-odd number
of data points, and median formula in the following sections.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 3

4. Median Definition
The value of the middle-most observation obtained after arranging the data in
ascending order is called the median of the data. Many an instance, it is difficult
to consider the complete data for representation, and here median is useful.
Among the statistical summary metrics, the median is an easy metric to calculate.
Median is also called the Place Average, as the data placed in the middle of a
sequence is taken as the median.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 4

5. Median Example
Let's consider an example to figure out what is median for a given set of data.
Step 1: Consider the data: 4, 4, 6, 3, and 2.
Let's arrange this data in ascending order: 2, 3, 4, 4, 6.
Step 2: Count the number of values. There are 5 values.
Step 3: Look for the middle value. The middle value is the median.
Thus, median = 4.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 5

6. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 6

7. ODD DATA
The age of the members of a weekend poker team has been listed below.
Find the median of the above set.
{42, 40, 50, 60, 35, 58, 32}
Solution:
Step 1: Arrange the data items in ascending order.
Original set: {42, 40, 50, 60, 35, 58, 32}
Ordered Set: {32, 35, 40, 42, 50, 58, 60}
Step 2: Count the number of observations. If the number of observations is
odd, then we will use the following formula: Median = [(n + 1)/2]th term
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 7

8. Step 3: Calculate the median using the formula.
Median = [(n + 1)/2]th term
= (7 + 1)/2th term = 4th term = 42
Median = 42
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 8

9. Even data
The height (in centimeters) of the members of a school football team have
been listed below.
{142, 140, 130, 150, 160,135, 158,132}
Find the median of the above set.
Solution:
Step 1:
Arrange the data items in ascending order.
Original set: {142, 140, 130, 150, 160, 135, 158,132}
Ordered Set: {130, 132, 135, 140, 142, 150, 158, 160}
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 9

10. Even data
Step 2:
Count the number of observations.
Number of observations, n = 8
If number of observations is even, then we will use the following formula:
Median = [(n/2)th term + ((n/2) + 1)th term]/2
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 10

11. Even data
Step 3:
Calculate the median using the formula.
Median = [(n/2)th term + ((n/2) + 1)th term]/2
Median = [(8/2)th term + ((8/2) + 1)th term]/2
= (4th term + 5th term)/2
= (140 + 142)/2
= 141
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 11

12. Median ( Discrete Data)
ExAMPLE 1 Calculate Arithmetic Median for the following discrete data −
Items ( X) Frequency ( f) cf
14 2
36 5
45 2
70 3
105 12
145 4
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 12

13. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 13

14. Example 2 Example
Let's calculate Arithmetic Median for the following discrete data −
Items ( X) Frequency ( f) cf
14 2
36 5
45 1
70 4
105 13
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 14

15. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 15

16. Example 3 Grouped data or continous data
Calculate the median for the following data:
Marks Number
0 - 10 6
10-30 20
30 - 60 37
60 - 80 10
80 - 90 7
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 16

17. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 17

18. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 18

19. Example 4 A surveyonthe heights (incm) of 50girls of class Xwas conductedata schoolandthe followingdata was obtained:
Height (incm) Numberofgirls
120-130 2
130-140 8
140-150 12
150-160 20
160-170 8
Findoutthe medianof givendata
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 19

20. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 20

21. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 21

22. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 22