3. What is Deciles
Deciles are measures of position calculated on a set of data.
The deciles are the values that separate a distribution into ten equal parts.
Formula
D =
𝐊
10 th data
∗ (n + 1)
Example:
The 10th, 20th, 30th, 40th, 50th, 60th, 70th, 80th, 90th and 100th percentiles
if you were in the 99th percentile for a particular test, that would put you in the decile ranking
of 10.
4. For Group data:
That can be calculated from the following formula
𝐷1 = 𝑙 +
𝑤
𝑓
(
𝑁
10
− 𝐶)
𝐷2 = 𝑙 +
𝑤
𝑓
(
2𝑁
10
− 𝐶)
𝐷9 = 𝑙 +
𝑤
𝑓
(
9𝑁
10
− 𝐶)
5. Where
L= Lower boundary of the class containing 𝐷2 to 𝐷9
W=Class interval size of class containing 𝐷2 or 𝐷9
F= is the frequency of the class containing 𝐷2 or 𝐷9
N=number of values
C=cumulative frequency
7. Quartiles
The value which the arranged data into four equal parts are called ... And it represented by
Q1,Q2,Q3
Understanding Quartiles
To understand the quartile, it is important to understand the median as a measure of central
tendency. The median in statistics is the middle value of a set of numbers. It is the point at
which exactly half of the data lies below and above the central value.
8. Step to find Quartile
Arrange the data in form of the lowest to highest
Find the median of the data value. This is the value of Q2
Find the median of data value the fall bellow Q2.this is the value for Q1
Find the median of the data value that fall above Q2.This is the value for Q3
9. Quartile Formula
First Quartile
𝐐1 = (
𝐧+1
4
)𝐭𝐡𝐓𝐞𝐫𝐦
Second Quartile
𝐐2 = (
𝐧+1
2
)𝐭𝐡𝐓𝐞𝐫𝐦
Third Quartile
𝐐3 = (
3(𝐧+1)
4
)𝐭𝐡𝐓𝐞𝐫𝐦
10. How to find Quartile Q1,Q2,Q3
Data
1,2,3,4,5,6,7,8,9,10,12
n=11
Q2=?
=(n+1)*50%
=(11+1)*0.5
=6
The number which is at 6th position is Q2 which is 5 is median.
11. Inter quartile range
The interquartile range is a measure of where the “middle fifty” is in a data
set. Where a range is a measure of where the beginning and end are in a
set, an interquartile range is a measure of where the bulk of the values
lie. That’s why it’s preferred over many other measures of spread
Formula
IQR= Upper Quartile − Lower Quartile
12. Central tendency
A measure of central tendency is a single value that attempts to describe a set of data by
identifying the central position within that set of data.
For example, suppose your earnings for the past week were the values shown in Table
