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