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प्रश्न
Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in an ascending order. The median of the data is 24. Find the value of x.
उत्तर
Given observations are 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43.
Here, total number of given observations, n = 10 ...(Even)
Since, n is even, so we use the formula for median,
Median = `((n/2)"th observation" + (n/2 + 1)"th observation")/2`
= `((10/2)"th observation" + (10/2 + 1)"th observation")/2` ...[Put n = 10]
= `(5"th observation" + 6"th observation")/2`
⇒ `24 = ((x + 1) + (2x - 13))/2` ...[Given]
⇒ 3x – 12 = 48
⇒ 3x = 60
⇒ x = 20
Hence, the value of x is 20.
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