numerical method in statistics (MEAN AND MEDIAN)

NUMERICAL METHOD

REPORTED BY:Angel Grace Adem

MEAN( )FORMULA:

Ungrouped Data :

Group Data:

where: f = frequency in each class

x= midpoint of each class n= total number of scores

MEAN( )EXAMPLES (ungrouped Data):

1. Find the mean of 5, 7, 11, 20 and 18.SOLUTION:

12.2

MEAN( ) 2. Find the Weighted Arithmetic mean of the numbers 12, 15, 16,12, 15, 18, 18, 20, 12 and 18.SOLUTION:

= = 15.6

MEAN( ) 3. The class standing of a student is 84, while the preliminary examination is 75. Compute the preliminary grade if the weighted of the class standing is 2 and the preliminary examination is 1.

MEAN( )SOLUTION:

82.33

MEAN( )Example (grouped data):1. SOLUTION:

5.636 or

5.64

Interval

Midpoint

Frequency

()

1-3 2 7 14

4-6 5 12 60

7-9 8 14 112

n=33

MEAN( ) 2. On arriving in the Beach of Boracay, a sample of 60 vacationers is asked about their ages by the Tourist Bureau. The Sample information is organized into the following frequency distribution. Compute the mean age.

SOLUTION:

42.33

AgeNo. of

Vacationer ()

Midpoint(x)

()

11-20 5 15.5 77.5

21-30 7 25.5 178.5

31-40 12 35.5 426

41-50 22 45.5 1001

51-60 8 55.5 444

61-70 4 65.5 262

71-80 2 75.5 151

n=60

MEAN( )3. Compute the new salary of the 20 employees in the ABC Company organized in the frequency distribution as follows:

SOLUTION:

295.5

Salary of Employee

sx ()

101-200 4 150.5

602

201-300 9 250.5

2254.5

301-400 3 350.5

1051.5

401-500 2 450.5

901

501-600 2 550.5

1101

n=20

MEDIAN

FORMULAGrouped Data :

Where: =lower class containing the median = less than cumulative frequency = frequency of the class containing median c = width of the class n = number of sample

MEDIAN

FORMULA (ungrouped data):

Where:

n= number of sample

MEDIAN

EXAMPLE 1. Following distribution of Mathematics scores of 20

students:

4.5 4.5

6

Scores

Number of

Students

CF

1-2 1 1

3-4 3 4 = 4

5-6 8 12 = 4.5

7-8 6 18

9-10 2 20