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A statistical term describing a division of observation based upon the values of the data is called quartile. The middle number between the lowest number and the median of the data set is first quartile (Q_{1}), the median of the data is second quartile (Q_{2}) and the middle value between the median and the highest value of the data set is third quartile (Q_{3}).
The lower quartile(Q_{1}) is a point which has 25% observation below it and 75% observations above it. The upper quartile (Q_{3}) is a point of 75% observation below it and 25% observation above it.
Note:
The quartiles divide the set of measurements into four equal parts. Twenty-five percent of the measurements are less than the lower quartile, fifty percent of the measurements are less than the median and seventy-five percent of the measurements are less than the upper quartiles So, fifty percent of the measurements are between the lower quartile and the upper quartile.
Example
Find the quartiles of the list:
10, 8, 6, 4, 12, 18, 20
Solution:
We need to put the given list in order:
4, 6, 8,1 0, 12,1 8, 20
First, we cut the list in half by finding the median.
The middle number is 10.
so, the median = 10
Now we look at the left half of the list (not including the median):
4, 6, 8 and we find its median.
Median of the left half = 6
Finally, we look at the right half of the list:
12, 18, 20 and we find its median
12, 18, 20 and we find its median. Median of the right half = 18
The quartiles are 6, 10, 18
Solution:
Arranging the data in ascending order.
8, 10, 12, 16, 25, 30, 35.
N=7
Now, Position of Q_{1}= (\(\frac{N+1}{4}\))^{th} item.
= (\(\frac{7+1}{4}\))^{th} item.
= 2^{th} item.
In given data 2^{th} item is 10.
Therefore, Q_{1} =10.
Solution:
Arranging, the data in ascending order.
10, 12, 16, 18, 20, 24, 28, 30, 40.
N=9
Now, Position of Q_{1} = (\(\frac{N+1}{4}\))^{th} item.
= (\(\frac{9+1}{4}\))^{th} item.
= (\(\frac{10}{4}\))^{th} item
= 2.5^{th} item.
Then, 2.5^{th} item lies in 2^{nd} and 3^{rd} item.
so, Q_{1}Median = \(\frac{12+16}{2}\)
= \(\frac{28}{2}\)
Therefore, Q_{1}= 14.
Solution:
Arranging the data in ascending order.
Now, 10, 12, 14, 16, 17, 20, 23.
N=7
Q_{1} = (\(\frac{N+1}{4}\))^{th} item.
= (\(\frac{7+1}{4}\))^{th} item
= 2^{th} item.
2^{th} item lies in 12.
Therefore, Q_{1} = 12.
Solution:
Arranging the data in ascending order.
9, 15, 21, 27, 33, 39, 45.
N=7
Now, Q_{3} =3(\(\frac{N+1}{4}\))^{th} item.
= 3(\(\frac{7+1}{4}\))^{th} item.
= 3\(\times\)2^{th} item
= 6^{th} item.
In given data 6^{th} item is 39.
Therefore, Q_{3} = 39.
Solution:
Arranging the data in ascending order.
14, 18, 22, 26, 30, 34, 38.
N= 7
Now, Q_{3} = 3(\(\frac{N+1}{4}\))^{th} item.
= 3(\(\frac{7+1}{4}\))^{th} item
= 3\(\times\)2
= 6^{th} item.
In the given data 6^{th} item is 34.
Therefore, Q_{3}= 34.
Solution:
Arranging the data in ascending order.
20, 30, 50, 60, 70, 80, 90.
N= 7
Now, Q_{3} = 3(\(\frac{N+1}{4}\))^{th} item.
= 3(\(\frac{7+1}{4}\))^{th} item
= 3\(\times\)2
= 6^{th} item.
In given data 6^{th} item is 80.
Therefore, Q_{3} = 80.
Solution:
Arranging the data in ascending order.
27, 29, 18, 25, 32, 21, 26.
N= 7
Now, Q_{1}= (\(\frac{N+1}{4}\))^{th} item.
=( \(\frac{7+1}{4}\))^{th} item
= \(\frac{8}{4}\)^{th} item.
= 2^{th} item.
Therefore, 2^{th} item is 29.
Solution:
Arranging the data in ascending order.
18, 21, 25, 26, 27, 29, 32
N= 7
Now, Q_{1}= (\(\frac{N+1}{4}\))^{th} item.
=( \(\frac{7+1}{4}\))^{th} item
= \(\frac{8}{4}\)^{th} item.
= 2^{th} item.
Therefore, 2^{th} item is 21.
Solution:
Arranging the data in ascending order.
28, 32, 34, 45, 54, 60, 67,
N=7
Now, Q_{3} = 3(\(\frac{N+1}{4}\))^{th} item.
= 3(\(\frac{7+1}{4}\))^{th} item.
= 3\(\times\)2
= 6^{th} item.
In the given data 6^{th} item is 60.
Therefore, Q_{3} = 60.
^{}
Solution:
Arranging the data in ascending order.
4, 6, 8, 10, 12, 18, 20.
N=7
Now, Q_{1} = (\(\frac{N+1}{4}\))^{th} item.
= (\(\frac{7+1}{4}\))^{th}item.
= \(\frac{8}{4}\)^{th} item.
= 2^{nd}item.
In the given data, 2^{nd} item is 6.
Therefore, Q_{1} = 6.
Solution:
Here,
Years(x) | Number of Students(f) | c.f |
8 | 3 | 3 |
10 | 5 | 3+5=8 |
12 | 7 | 8+7=15 |
14 | 8 | 15+8=23 |
16 | 3 | 23+3=26 |
18 | 1 | 26+1=27 |
Total | N= 27 |
Here, N=27
Now, Q_{3} = 3(\(\frac{N+1}{4}\))^{th} item.
= 3(\(\frac{27+1}{4}\))^{th} item.
= 3\(\times\)7
= 21^{st}item.
In the given data 21item lies in 14 years.^{st}item lies in 14 years.
Therefore, Q_{3} = 14
If 12, 3x - 1, 20, 28, 34, 40, 44 are in ascending order having the first quartile 17, find the value of x.
Find the quartile(Q_{1}) from the following data:
28, 7, 2, 14, 20, 12, 24.
Find the Quartile(Q_{1}) from the following data.
16, 10, 12, 18, 20, 14, 30, 28, 40.
Find the Quartile(Q_{1}) from the following data:
15, 13, 18, 16, 14, 17, 12
Find the Quartile(Q_{3}), from the following data:
27, 29, 18, 25, 32, 21, 26
Find the Quartile(Q_{3}) from the following data:
46, 64, 82, 75, 70, 68, 55
If 10, 16, 22, 24, 28 , 2a - 3, 37 are in ascending order having third quartile 31, Find the value of a?
Find the Quartile(Q_{1}) from the following data:
72, 61, 52, 68, 56, 50, 64.
Find the Quartile(Q_{3}), from the following data:
10, 8, 6, 4, 12, 18, 20
Find Quartile (Q_{2}) from the following data:
28, 6, 25, 10, 24, 30, 12
Find the Quartile(Q_{2}), from the following data:
35, 5, 30, 25, 20, 15
Find Quartile (Q_{1}), from the following data:
10, 18, 12, 30, 22, 14, 13
Find the Quartile(Q_{3}), from the following data:
7, 17, 9, 12, 22, 18, 20
Find the Quartile(Q_{2}), from the following data:
13, 45, 23, 33, 43, 19, 25
Find the Quartile(Q_{1}), from the following data:
42, 15, 28, 33, 18, 40, 27
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