In statistics, linear interpolation is often used to find the estimated median, quartiles or percentiles of a set of data and particularly when the data is presented in a group frequency table with class intervals. In this article we will look at how to do a linear interpolation calculation with the use of a table and graph to find the median, 1st quartile and 3rd quartile.

1. Solving
Quartile using
Linear
Interpolation
Method

2. LINEAR INTERPOLATION
is the simplest method of
finding a value between two
points. It is given by:
Lower Value + [decimal part(Higher
value – Lower Value)]

3. 1. Find , , and given the following scores
using linear interpolation.
2, 10, 3, 8, 12, 15, 4, 9, 13
2, 3, 4, 8, 9, 10, 12, 13, 15
k = 1
n = 9
Let’s proceed to
linear
interpolation

4. Steps of Linear Interpolation
Therefore the
value of
a. Q1 = 2nd
data +0.5[3rd
– 2nd
]
= 3 + 0.5[4 – 3]
= 3 + 0.5 (1)
= 3 + 0.5
2, 3, 4, 8, 9, 10, 12, 12, 13, 14 15, 16

5. 1. Find , , and given the following scores
using linear interpolation.
2, 10, 3, 8, 12, 15, 4, 9, 13
2, 3, 4, 8, 9, 10, 12, 13, 15
k = 2
n = 9
No need linear
interpolation
Therefore the
value of

6. 1. Find , , and given the following scores
using linear interpolation.
2, 10, 3, 8, 12, 15, 4, 9, 13
2, 3, 4, 8, 9, 10, 12, 13, 15
k = 3
n = 9
Let’s proceed to
linear
interpolation

7. Steps of Linear Interpolation
𝑄3=7 .5 h
𝑡
2, 3, 4, 8, 9, 10, 12, 13, 15
Therefore the value
of
Q3 = 7th
data +0.5[8th
– 7th
]
= 12 + 0.5[13 – 12]
= 12 + 0.5 (1)
= 12 + 0.5

8. FIRST FIVE
Find the 3rd
quartile of the following
test scores of a random samples of
eleven students. Use interpolation if
the result is a decimal number.
30, 37, 35, 23, 10, 18,
8, 28, 15, 13, and 23.

9. Arrange the data in ascending order.
Q3 = 30
8, 10, 13, 15, 18, 23, 23, 28, 30, 35, 37
Q3 =
=
=
Position of Q3= 9 (9th
data)

10. 1. Using the scores of Grade 10
students in their 30-item test in Math,
compute the lower quartile, median,
upper quartile and the interquartile
range of the given data set. Use
linear interpolation, when the result is
a decimal number. Show your
solutions.
21 15 22 30 25 16 22 19
ASSIGNMENT

11. THANK YOU
FOR
LISTENING!