**Quartile**

**Is the score points which divide a distribution into four equal parts**

Twenty - five percent (25%) of the distribution of the data are below the first quartile

**Mendenhall and Sincich Method**

This method is being developed by William Mendenhall and Terry Sincich to find the position of the quartile in the given data.

Example No.1

The owner of a coffee shop recorded the number of customers who came into his cafe each hour in a day. The result were 14, 10, 12, 9, 17, 5, 8, 9, 14, 10 and 11. Find the lower quartile and the upper quartile

Example no. 2:

Find the first quartile, second quartile and third quartile given the score of ten students in their mathematical activity

**To solve the quartile of the given data here are the following steps:**

Arrange the data in ascending order or to the lowest value to the highest value in the data

**Quartile for Ungrouped Data**

Fifty percent (50%) are below the second quartile. The second quartile is called the MEDIAN

Seventy - five percent (75%) are below the third quartile

To find the quartile in a given data Mendenhall and Sincich use the following formula:

Third, find the least value of the data and the greatest value of the data

Fourth, find the lower quartile of the given data using the method of Mendenhall and Sincich Method in finding the lower quartile

Fifth, find the middle value of the data or the median in the given data. To find the median of the data, use the Mendenhall and Sincich Method.

Lastly, find the upper quartile of the given data. To find the upper quartile, use the formula below.

The interquartile range is the difference between the upper quartile and the lower Quartile

Solution:

Find the ascending order of the data.

The Ascending Order of the Data is:

5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17

Then Find the Least Value of the Data and the Greatest Value of the DAta

The Least value of the data is 5 and the greatest value of the data is 17

Find the lower quartile in the data using the Method of Mendenhall and Sincich.

Using the Formula

Find the middle value in the data using the formula

Lastly to find the upper quartile in the given data, using:

4, 9, 7, 14, 10,8,12,15,6,11

Prepared by:

Ramos, Lemuel Louis B.

Quartile for Ungrouped Data

Reference:

file:///C:/Users/Administrator/Downloads/Math10_TG_U4.pdf

http://study.com/academy/lesson/upper-quartile-definition-formula.html

Mathematics Learner's Module Pages 362 - 372

N is the number of elements in the Data

Example:

the manger of an food chain recorded the number of customers who came to eat at there products in each our of the day. The results were 10, 15, 14, 13, 20, 19, 12, and 11. How many elements are in the data?

Second, find the n or the number of elements present in the data

find the n or the number of elements in the data

The number of elements present in the data is 11 or n = 11

Q1 = (n+1)

Q1 = (11+1)

Q1 = (12)

Q1 =

Q1 = 3

Therefore the Q1 is the third element in the data,

so the Q1 is 9.

Q2 = (n+1)

Q2 = (11+1)

Q2 = (12)

Q2 = 24 / 4

Q2 = 6

Therefore the Q2 is the sixth element in the data,

so the Q2 is 10.

Q3 = (n+1)

Q3 = (11+1)

Q3 = (12)

Q3 =

Therefore the Q3 is the ninth element of the data, so the Q3 is 14.

Q3 = 9

Solution:

Find ascending order of the data

The ascending order of the data is 4,6,7,8,9,10,11,12,14,15

Find the n or the number of elements present in the data

The number of elements present in the data is 10

or n = 10

find the least value of the data and the greatest value of the data

The least value in the data is 4 and the

greatest value in the data is 15.

Find the lower quartile of the given data using

Q1 = (n+1)

Q1 = (10+1)

Q1 = (11)

Q1 =

Since the Q1 is 2.75, it will be round up.

Therefore the Q1 is the third element in the data,

so the Q1 is 7

Q1 = 2.75

Find the middle value of the data using the formula

Q2 = (n+1)

Q2 = (10+1)

Q2 = (11)

Q2 = 22/4

Therefore the Q2 is the average of the 5th and 6th element in the data. to find it we will add the 5th and 6th element in the data, after we will divide it by two. so the Q2 will be 9.5.

Q2 = 5.5

Find the upper value of the given data using the formula

Q3 = (n+1)

Q3 = (10+1)

Q3 = (11)

Q3 = 33/4

Q3 = 8.25

Since the Q3 is 8.25, it will be round down. Therefore the Q3 is the eighth element in the data, so the Q3 is 12.

5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17

5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17

5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17

5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17

4,6,7,8,9,10,11,12,14,15

5, 8, 9, 9, 10, 10, 11, 12, 14, 14, 17