1. NUMERICAL METHOD
REPORTED BY:
Angel Grace Adem

2. MEAN( 𝑥 )
FORMULA:
Ungrouped Data :
𝑥 =
𝑥1+𝑥2+⋯ 𝑥 𝑛
𝑛
Group Data:
𝑥 =
𝑓𝑥
𝑛
where: f = frequency in each class
x= midpoint of each class
n= total number of scores

3. MEAN( 𝑥 )
EXAMPLES (ungrouped Data):
1. Find the mean of 5, 7, 11, 20 and 18.
SOLUTION:
𝑥 =
5 + 7 + 11 + 20 + 18
5
=
61
5
= 12.2

4. MEAN( 𝑥 )
2. Find the Weighted Arithmetic mean of the
numbers 12, 15, 16,12, 15, 18, 18, 20, 12 and
18.
SOLUTION:
𝑥 =
12 3 +15 2 +18 3 +16+20
3+2+3+1+1
=
36+30+54+36
10
=
156
10
= 15.6

5. MEAN( 𝑥 )
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.

6. MEAN( 𝑥 )
SOLUTION:
𝑥 =
2
3
84 +
1
3
79
=
168
3
+
79
3
=
247
3
= 82.33

7. MEAN( 𝑥 )
Example (grouped data):
1. SOLUTION:
𝑥 =
𝑓𝑥
𝑛
𝑥 =
186
33
𝑥 = 5.636 or
5.64
Interv
al
Midpoint Frequen
cy
(𝒇𝒙)
1-3 2 7 14
4-6 5 12 60
7-9 8 14 112
n=33 𝑓𝑥 = 186

8. MEAN( 𝑥 )
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:
𝑥 =
𝑓𝑥
𝑛
𝑥 =
2540
60
𝑥 =42.33
Age
No. of
Vacatione
r (𝒇)
Midpoint
(x) (𝒇𝒙)
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 𝑓𝑥 = 2540

9. MEAN( 𝑥 )
3. Compute the new salary of the 20 employees in the ABC Company
organized in the frequency distribution as follows:
SOLUTION:
𝑥 =
𝑓𝑥
𝑛
𝑥 =
5910
20
𝑥 =295.5
Salary of
Employees
𝒇
x
(𝒇𝒙)
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 𝑓𝑥 = 5910

10. MEDIAN 𝑥
FORMULA
Grouped Data :
𝑥 = 𝐿 𝑏 +
𝑛
2
−𝐶𝐹<
𝑓 𝑚
∙ 𝑐
Where: 𝐿 𝑏 =lower class containing the median
𝐶𝐹< = less than cumulative frequency
𝑓𝑚 = frequency of the class containing median
c = width of the class
n = number of sample

11. MEDIAN 𝑥
FORMULA (ungrouped data):
𝑥 =
𝑛+1
2
Where:
n= number of sample

12. MEDIAN 𝑥
EXAMPLE 1.
Following distribution of Mathematics scores of 20 students:
𝒙 = 𝑳 𝒃 +
𝒏
𝟐
−𝑪𝑭<
𝒇 𝒎
∙ 𝑐
𝒙 = 4.5 +
𝟐𝟎
𝟐
−𝟒
𝟖
∙ 𝑐
𝒙 = 4.5 +
10−4
8
⋅ 2
𝒙 = 6
Scores
Number
of
Students
CF
1-2 1 1
3-4 3 4 𝐶𝐹< =
4
5-6 8 12 𝐿 𝑏 =
4.5
7-8 6 18
9-10 2 20