Finding quartile

Question

How do I find first second and third quartiles...I know the definition I need to know how to find them

 

Stem.     Leaf

2             77

5             7799

6             0246

8             3368

9             22269

10           00224

Answer 1

Put your numbers in order

(27, 27, 57, 57, 59, ...)

Divide them into 4 same-sized groups.

There are 24 numbers in the dataset, so it divides into 4 groups with 6 values in each one.

 

Since the dividing lines between fourths (quarters) all lie between two numbers (for example, between the 6th and 7th numbers), the quartiles are the average of the end of one group and the first number in the next group.

 

I get the first group ending at 59

The second group starts at 60.

The first quartile is Q1 = (59+60) / 2 = 59.5

 

The other group divisions occur between:

83 and 86  Q2 = 84.5

96 and 99  Q3 = 97.5

 

If the numbers don't divide into equal groups, the procedure is different.

If the the dividing line is right in the middle of a number, that number is quartile value.

When the dividing line is some fraction of the way between two numbers, you would have to calculate a weighted average.  That's a little messy and probably beyond the scope of what you're learning right now.  This particular problem has divisions in the middle between two numbers each time, so those two numbers have equal weights.  That's why a simple average does the trick.