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If the median of a list of numbers is m, the first quartile

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If the median of a list of numbers is m, the first quartile [#permalink] New post   15 May 2016, 11:00
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If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35 ?

A) 33

B) 28

C) 27

D) 24

E) 23
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Bunuel
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   15 May 2016, 11:08
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HKD1710 wrote:
If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35 ?

A) 33

B) 28

C) 27

D) 24

E) 23


The median of {19, 22, 24, 26, 30, 33, 35, 42} is 28.

The numbers less than the median are {19, 22, 24, 26}. The median of this list is 23.

Answer: E.
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   15 May 2016, 11:09
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HKD1710 wrote:
If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35 ?

A) 33

B) 28

C) 27

D) 24

E) 23


It is given that a quartile is the middle number of all numbers less than median..

so lets arrange the number in ascending order- 42, 24, 30, 22, 26, 19, 33 and 35
19, 22, 24, 26, 30 , 33, 35, 42...

numbers less than median are 19, 22, 24, 26..
the median of these numbers = center of 22 and 24 = 23
E
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   15 Oct 2016, 09:11
rearrange numbers (lowest - highest)

19 22 24 26 30 33 35 42

Notice that since we have an even number we go to the center of the list --> add 26 & 30, divide by 2 = 28 (Median of the set)

Numbers in list less than 28 are as follows: 19 22 24 26 --> Median of these = (22+24)/2 = 23

Thus, E is the correct answer.
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   28 Nov 2019, 06:18
Arrange the number to find the median
19, 22, 24, 26 ,30,33,35,42. m = 28
And then arrange the numbers less than 28
19,22,24,26 , first quartile = 46/2 = 23.

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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   29 Nov 2019, 08:19
HKD1710 wrote:
If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35 ?

A) 33

B) 28

C) 27

D) 24

E) 23


Sort the list: 19, 22, 24, 26, 30, 33, 35, 42

Median of that list: (26+30)/2 = 28

List that are less than m: 19, 22, 24, 26
Median of the above list = (22+24)/2 = 23

ANSWER: E
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   10 Jul 2020, 11:17
What is a quartile?
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   02 Dec 2020, 00:06
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1st sentence is indeed redundant
anyone can find the 1st quartile from the given set

Quartile means dividing the whole set of numbers into four parts
19, 22, 24, 26, 30, 33, 35, 42

19, 22,(Q1) 24, 26,(Q2 or Median) 30, 33,(Q3) 35, 42

Q1=23
Q2=28
Q3=34

ANSWER: E
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   02 Dec 2020, 06:15
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Arrange the data in ascending order: 19 22 24 26 30 33 35 42

Median: \(Q_2\) : \(\frac{(26 + 30)}{2}\) = 28

First Quartile \(Q_1\): Data series has numbers less than Median(28): 19 22 24 26

\(Q_1\): \(\frac{(22 + 24)}{2}\) = 23

Answer E
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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   01 Jan 2021, 15:34
Quartile mean dividing the set into 4 equal parts.
Q1= 19,22
Q2=24,26
Q3=30,33
Q4=35,42

is this not the right way to divide the set into 4 equal parts. Where am i wrong?
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If the median of a list of numbers is m, the first quartile [#permalink] New post   19 Oct 2022, 10:22
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Given that the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. And we need to find What is the first quartile of the list of numbers 42, 24, 30, 22, 26, 19, 33 and 35

This problem is from a topic called as Box and Whisker Plot

Let's arrange the set in ascending order first. We get the set as

19, 22, 24, 26, 30, 33, 35, 42 => 8 values are there

=> Median will be the mean of the middle two terms = \(\frac{26 + 30}{2}\) = 28

(Watch this Video to know more about Medians and Statistics)

Now, the first half of the set will be 19, 22, 24, 26

=> First Quartile or \(Q_1\)= Median of first half = mean of middle two values = \(\frac{22 + 24}{2}\) = 23

So, Answer will be E.
Hope it helps!

wali786: Please watch the below video to know how to divide the set into Quartiles.

Watch the following video to learn the Basics of Box and Whisker Plot

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Re: If the median of a list of numbers is m, the first quartile [#permalink] New post   12 Nov 2023, 23:07
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