Data
Analysis
Prepared by:
Cielito V. Maligalig, MEP CE, RCE
Type of Data
• Ungrouped Data
• Grouped Data
Measure of
Central
Tendency
Mean
• Average value of all data in the set.
Median
• A value that subdivide exactly the set
data into two parts.
Mode
• Value that occurs most frequently.
• Ungrouped Data
Type of Data
• 4, 8, 10, 14, 18, 19, 23, 24
• 4, 6, 9, 10, 12, 15, 17, 20 28
• Grouped Data
•𝑥=
Mean
Ungrouped
𝑥𝑖
𝑛
( Mean)
• Weighted Mean
• 𝑥 = 𝑤𝑥/ 𝑤
• Where:
• 𝑥 = 𝑚𝑒𝑎𝑛
• n = number of observation
• w = weight of each observation
• 𝑥 = 𝑥𝑛+1 (odd number of data)
2
Median
•𝑥=
𝑥𝑛 + 𝑥𝑛
2 +1
2
2
𝑒𝑣𝑒𝑛 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑡𝑎
• Where:
• 𝑥 = 𝑚𝑒𝑑𝑖𝑎𝑛
• 𝑥𝑖 = 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑑𝑎𝑡𝑎
Mode
•𝑥=𝑥
• Where:
• 𝑥 = 𝑚𝑜𝑑𝑒
• x = observed data which most frequently
occur
•𝑥=
Mean
Grouped
𝑓𝑥𝑖
𝑛
( Mean)
• Where:
• 𝑥 = 𝑚𝑒𝑎𝑛
• f = frequency
• n = number of observation
• By coding or deviation
• 𝑥 = 𝑥0 +
𝑓𝑑
𝑛
𝑐
• Where:
• xo = class mark
• d = code or deviation
• c = class interval
𝑛
• 𝑥 = L𝑏 +
Median
( 2 − ≺𝐶𝐹)
𝑓𝑚
𝑐
• WHERE:
• 𝑥 = 𝑚𝑒𝑑𝑖𝑎𝑛
• 𝑛 = 𝑡𝑜𝑡𝑎l 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛
• Lb = lower limit
• <CF = cumulative frequency before the
median class
• fm = frequency of the median class
• c = class interval
•𝑥=
Mode
•
•
•
•
•
𝑓𝑚𝑜 −𝑓1
𝐿𝑚𝑜 + (
)𝑐
2𝑓𝑚𝑜 −𝑓1− 𝑓2
Where:
𝑥 = 𝑚𝑜𝑑𝑒
Lmo = Lower limit of the modal class
fmo = frequency of the modal class
f1 = frequency of the class before the modal
class
• f2 = frequency of the class after the modal
class
•
•
Quartile,
Decile &
Percentile
Ungrouped
•
𝑛𝑁
𝑄𝑛 =
4
𝑛𝑁
𝐷𝑛 =
10
𝑛𝑁
𝑃𝑛 =
100
• Where:
• Qn = Quartile
• Dn = Decile
• Pn = Percentile
• N = number of observed data
• n = nth quartile, decile or percentile
• 𝑄𝑛 = 𝐿𝑏 +
• 𝐷𝑛 = 𝐿𝑏 +
Quartile,
Decile &
Percentile
Grouped
• 𝑃𝑛 = 𝐿𝑏 +
𝑁
4
( −<𝑐𝑓)
𝑓𝑄𝑛
𝑐
𝑁
10
( −<𝑐𝑓)
𝑓𝐷𝑛
(
𝑁
−<𝑐𝑓)
100
𝑓𝑃𝑛
𝑐
𝑐
• Where:
• Qn = Quartile
• Dn = Decile
• Pn = Percentile
• N = number of observed data
• n = nth quartile, decile or percentile
• Lb = lower limit
• <cf = cumulative frequency before the quartile, decile and percentile class
• f(Qn, Dn, Pn) = frequency of quartile, decile or percentile class.
• c = class interval
Example
• From the given data determine the
mean, median, mode, quartile, decile
and percentile.
• 53, 48,76, 64, 79, 81,
62, 43, 63,
76, 41, 53
• 53, 48,76, 64, 79, 81,
62, 43, 63,
76, 41, 53, 72
• From the given data determine the
mean, median, mode, quartile, decile
and percentile.
Example
Class
F
48 – 52
7
53 – 57
4
58 – 62
5
63 – 67
12
68 – 72
16
73 – 77
9
78 – 82
11
83 – 87
2
88 – 92
13
93 – 97
1
Lb
Ub
< cf
Xc
--