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16. If the median of the data: 6,7, x-2, x, 17, 20, written in ascending order, is 16. Then x= (d) 30 (a) 15 (b) 16

Question

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## Answers ( )

AnswerGiven : Median = 16 , observations are arrange in ascending order : 6, 7, x − 2, x, 17, 20

Total number of observations = 6

n = 6 (even)

If n is even then median = ½value of [ (n/2)th + (n/2 +1) th] observations.

Median = ½[(6/2)th + (6/2 + 1) th] observations

Median = ½ [3th + 4th] observations

16 = ½ [(x – 2) + x

16 × 2 = 2x – 2

32 = 2x – 2

2x = 32 + 2

2x = 34

x = 34/2 = 17

x = 17

Hence, the value of x is 17.

★★ Median of the data depends on the number of observations (n) .

i) If n is odd then median= value of [(n+1)/2]th observation

ii) If n is even then median= ½value of [ (n/2)th + (n/2 +1) th] observations.

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Answer:answer……………….17