what is a Quartile? for math?

Question

Find the lower quartile of {2, 4, 16, 25, 29}.
16
3
27
25

Answer 1

Quartile
A statistical term describing a division of observations into four defined intervals based upon the values of the data and how they compare to the entire set of observations.

Each quartile contains 25% of the total observations. Generally, the data is ordered from smallest to largest with those observations falling below 25% of all the data analyzed allocated within the 1st quartile, observations falling between 25.1% and 50% and allocated in the 2nd quartile, then the observations falling between 51% and 75% allocated in the 3rd quartile, and finally the remaining observations allocated in the 4th quartile.
http://www.investopedia.com/terms/q/quartile.asp

Upper and Lower Quartiles
The Lower Quartile Q1 is that number such that 25% of observations are less than it and 75% are larger, or to be more precise, at least 25% of the sorted values are less than or equal to Q1 and at least 75% of the values are greater than or equal to Q1.
The Upper Quartile Q3 is that number such that 75% of observations are less than it and 25% are larger, or to be more precise, at least 75% of the sorted values are less than or equal to Q3, and at least 25% of the values are greater than or equal to Q3.

Following this notation, the median should actually be called the "middle quartile" Q2, since it is that number such that 50% are less than it and 50% are larger.

NOTE: To find the quartiles, you must first sort your data (similar to finding the mean).




Find the lower quartile of {2, 4, 16, 25, 29}.(This has 5 numbers).

L1 = 0.25 * 5 = 1.25, which gets rounded up to 2. Thus, I take the number in the 2nd position to be the lower quartile

lower quartile = 4

L3 = 0.75 * 5 = 3.75, which gets rounded up to 4. Thus, I take the 4th number (i.e. 25) to be the upper quartile.

upper quartile = 25

median = 16

Answer 2

2 and 4

Answer 3

The Upper extreme is highest;
lower extreme is lowest,
median is middle,
Upper quartile is averge of the upper extreme to the number above the median ,
and lower quartile is the average of lower extreme to the number below the median.
So take the lower exterme & average it with the nubers below the median, which is only 4.
2+4= 6
6/2= 3
3 is the lower quartile.

Answer 4

first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile

so im guessing its 3!

Answer 5

Quartile indicates a quarter. As in: the top 25% = top quartile.

Answer 6

For a recent standardized test, the median was 88, Q1 was 67, and Q3 was 105. Describe the following scores in terms of quartiles.

a) 8

b) 81

c) 103

a Q1 since it is between 0 and 67
b Q2 since it is between 67 and 88
c Q3 since it is between 88 and 105

Answer 7

4

Min=2
1st Quartile=4
median=16
3rd quartile=25
Max=29

that's the five number summary for those five numbers.