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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Statistics

NTA Abhyas 2020 · Mathematics · Statistics

A number equal to 2 times the mean and with a frequency equal to k...

A number equal to 22 times the mean and with a frequency equal to kk is inserted in a data having nn observations. If the new mean is 43\dfrac{4}{3} times the old mean, then the value of kn\dfrac{k}{n} is

Correct answer

0.5

Step-by-step solution

x¯new=43x¯{\overset{¯}{x}}_{new} = \dfrac{4}{3}\overset{¯}{x}
From given information
x¯new=nx¯+2kx¯n+k=43x¯{\overset{¯}{x}}_{new} = \dfrac{n\overset{¯}{x} + 2k\overset{¯}{x}}{n + k} = \dfrac{4}{3}\overset{¯}{x}
⇒3n+6k=4n+4k⇒ 3n + 6k = 4n + 4k
⇒2k=n⇒ 2k = n
⇒kn=0.5⇒ \dfrac{k}{n} = 0 . 5
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