Question

25. What is the value of Q1 for the following data?
25, 28, 20,30,33,38, 22, 26.​

Answer 1

Answer:

Solution

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Correct option is

A

27.5

25,34,31,23,22,26,35,29,20,32

No' of observations (n) =10

first of all we arrange the observations in an ascending order

20,22,23,25,26,29,31,32,34,35

Here observe that No' of observations (n) is even so

Median is average of

2

n

th term and (

2

n

+1) th term

Median =

2

2

n

th term+(

2

n

+1)th term

=

2

2

10

th term+(

2

10

+1)th term

=

2

5th term+6th term

=

2

26+29

=

2

55

Median = 27.5

Answer 2

Value of Q1

The value of Q1 for the given set of observations is  23.5

Explanation:

Arrange all the observations in ascending order as follows

20,22,25,26,28,30,33,38

Now, find the median of the given set of observations. Since, we have even number of observations the median will be the average of 26 and 28.

Median = (26+28)/2

             = 27

Now, according to the median we divide our set of observations into two sets. One will be the set of observations lesser than the median and the other will be the set of observations greater than the median.

Accordingly, we have:

Lower set = (20,22,25,26)

Higher set = (28,30,33,38)

Now, our Q1 is the median of the lower set

Therefore, Q1 = (22+25)/2

                       = 23.5

Therefore, the value of Q1 is 23.5