Question

What is the first quartile,Q1, of the data set?

{23, 28, 28, 36, 56, 60, 61, 65, 70}



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Q1 =

Answer 1

Answer:
`Q_1=28`

Explanation:

Given data :-{23, 28, 28, 36, 56, 60, 61, 65, 70}

The number of observations n =9

We know that the position of median is given by :-

`Q_1=(n+1)/(4)^(th)\text{ item}`

Now, for n=9,

`Q_1=(9+1)/(4)^(th)\text{ item}=(10)/(4)^(th)\text{ item}=2.5^(th)\text{ item}\\\\=2^(th)\text{ item}+0.5(3^(th)\text{ item}-2^(th)\text{ item})\\\\=28+0.5(28-28)\\\\=28+0.5(0)=28\\\\\Rightarrow\ Q_1=28`

Answer 2

Quartile 1 is 28

Explanation:

We are given aa data set

23, 28, 28, 36, 56, 60, 61, 65, 70

We have to calculate the I quartile

The data is arranged already in ascending order

Median is the middle entry = 5th entry = 56

Q1 = I quartile = median of the 5 entries

= 3rd entry

=28

Hence answer is

Q1 =28