dfhh

2. Ungrouped Data
 Measures Of Dispersion or Variation
Grouped data
 Measures of Central Tendency
 Measures of central/non central position

3. MEASURE OF DISPERSION OR VARIATION
- indicate how the observations are scattered or
dispersed about the average.
1.Range
2.Variance
3.Standard Deviation
4.Coefficient of Variation

4. Range
– the difference between the highest value
and the smallest value in the data set.
R = (Highest value – Lowest value)

5. Variance
- Is the average of the squared deviation from the
mean.
𝜎2 =
𝑖=1
𝑁
(𝑥𝑖 − 𝜇)2
𝑁
𝑓𝑜𝑟 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛
𝑠2 =
𝑖=1
𝑛
(𝑥𝑖 − 𝑥)2
𝑛 − 1
𝑓𝑜𝑟 𝑠𝑎𝑚𝑝𝑙𝑒

6. Standard Deviation
- Is the positive square root of the average of
the squared deviation from the mean.
For Population: 𝜎 = 𝜎2
For Sample : 𝑠 = 𝑠2

7. Coefficient of Variation
- Is the ratio of the standard deviation to the
mean.
For Population: 𝐶𝑉 =
𝜎
𝜇
× 100%
For Sample : 𝐶𝑉 =
𝑆
𝑋
× 100%

8. MEASURES OF CENTRL TENDENCY FOR
GROUPED DATA
 Arithmetic Mean
𝜇 = 𝑖=1
𝑘
𝑓 𝑖 𝑥 𝑖
𝑖=1
𝑘
𝑓 𝑖
for population
𝑥 = 𝑖=1
𝑘
𝑓 𝑖 𝑥 𝑖
𝑖=1
𝑘 𝑓 𝑖
for sample

9. MEASURES OF CENTRL TENDENCY FOR GROUPED DATA
 Median ( 𝜇, 𝑥 )
𝜇 = 𝐿𝐶𝐵 𝑚 + 𝑐 [
𝑛
2
− 𝐹 𝑚−1
𝑓𝑚
]
𝑥 =𝐿𝐶𝐵 𝑚 + 𝑐 [
𝑛
2
−𝐹 𝑚−1
𝑓 𝑚
]
Where :
𝐿𝐶𝐵 𝑚 = is the lower class boundary of the median class
𝑐 = class width
𝐹 𝑚−1 = cumulative frequency before the cumulative frequency of the
median class.
𝑓𝑚 = frequency of the median class
n = number of observation

10. MEASURES OF CENTRL TENDENCY FOR GROUPED DATA
 Mode ( 𝜇, 𝑥 )
𝜇 = 𝐿𝐶𝐵 𝑚𝑜 + 𝑐 [
𝑓 𝑚0 − 𝑓1
2𝑓𝑚𝑜 − 𝑓1 − 𝑓2
]
𝑥 = 𝐿𝐶𝐵 𝑚𝑜 + 𝑐 [
𝑓 𝑚0 − 𝑓1
2𝑓𝑚𝑜 − 𝑓1 − 𝑓2
]
where
𝐿𝐶𝐵 𝑚𝑜= is the lower class boundary of the
modal class
c = the class width
𝑓 𝑚0 = frequency of the modal class
𝑓1 = frequency before the modal class
𝑓2 = frequency after the modal class.