Find the 3 quartiles in the following data set: 55, 55, 59, 60, 62, 65, 64

Solution:

The quartile formula helps to divide a set of observations into 4 equal parts.

The first quartile lies in the middle of the first term and the median.

The median is the second quartile.

The middle value lying between the median and the last term is the third quartile.

Mathematically, the quartiles are represented as follows,

1. First Quartile(Q₁) = ((n + 1)/4)th Term

2. Second Quartile(Q₂) = ((n + 1)/2)th Term

3. Third Quartile(Q₃) = (3(n + 1)/4)th Term

Given, the data is 55, 55, 59, 60, 62, 65, 64.

We have to find the 3 quartiles.

Now, arrange the data in ascending order.

55, 55, 59, 60, 62, 64, 65.

Here, n = 7

1) Q₁ = [(7 + 1)/4]th term

= 8/4

= 2nd term

Q₁ = 55

2) Q₂ = [(7 + 1)/2]th term

= 8/2

= 4th term

Q₂ = 60

3) Q₃ = [3(7 + 1)/4]th term

= [3(8)/4]

= 3(2)

= 6th term

Q₃ = 65

Therefore, the three quartiles are 55, 60 and 65.

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Find the 3 quartiles in the following data set: 55, 55, 59, 60, 62, 65, 64

Summary:

The 3 quartiles in the following data set: 55, 55, 59, 60, 62, 65, 64 are 55, 60 and 65.