Question

Let x be the median of the data:
34. 28, 20, 32, 15, 9, 23, 26, 35, 16, 33, 43.
If 16 and 23 are replaced by 30 and 32, respectively in the data, then let y be the median of the resulting
data. What is the value of (3x – 2y)?​​

Answer 1

Answer:

19

Step-by-step explanation:

First sort the element: Then median =(26+28)/2=27   so, x=27

Then replace the value of 16 and 23 with 30 and 32 Then again sort.

so y = (30+32)/2=31

(3x-2y)=3*27-2*31

y = 81-62=19

so, Answer = 19

Answer 2

Solution :-

Writing given data in ascending order we get :- 9, 15, 16, 20, 23, 26, 28, 32, 33, 34, 35, 43 = Total 12 terms .

So,

→ Median = [(12/2) th term + {(12/2) + 1} th term] / 2

→ Median = [6th term + 7th term]/2

→ x = (26 + 28)/2

→ x = 54/2

→ x = 27

now, 16 and 23 are replaced by 30 and 32 . Then, data in ascending order is :- 9, 15, 20, 26, 28, 30, 32, 32, 33, 34, 35, 43 .

So,

→ New median = [6th term + 7th term]/2

→ y = (30 + 32)/2

→ y = 62/2

→ y = 31

therefore,

→ (3x - 2y)

→ (3 * 27 - 2 * 31)

→ 81 - 62

→ 19 (Ans.)

Hence, required value is equal to 19 .

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