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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2020 · 6 September · Evening Shift · Mathematics · Statistics

Consider the data on x taking the values 0, 2, 4, 8, . . . . . , 2...

Consider the data on xx taking the values 0,2,4,8,.....,2n0, 2, 4, 8, . . . . . , {2}^{n} with frequencies C0n,C1n,C2n,....,CnnC0 n , C1 n , C2 n , . . . . , Cn n respectively. If the mean of this data is 7282n\dfrac{728}{{2}^{n}}, then nn is equal to ....... .

Correct answer

0

Step-by-step solution

xi{x}_{i} (observation) 0 2 22{2}^{2}................ 2n{2}^{n}
fi{f}_{i} (frequency) C0nC0 n C1nC1 n C2nC2 n............. CnnCn n

x¯=ΣfixiΣfi\overset{¯}{x} = \dfrac{Σ{f}_{i}{x}_{i}}{Σ{f}_{i}}

0×C0n+2×C1n+22×C2n.....2n×CnnC0n+C1n+C2n.....+Cnn=3n−12n=7282n\dfrac{0 \times C0 n + 2 \times C1 n + {2}^{2} \times C2 n . . . . . {2}^{n} \times Cn n}{C0 n + C1 n + C2 n . . . . . + Cn n} = \dfrac{{3}^{n} - 1}{{2}^{n}} = \dfrac{728}{{2}^{n}}

⇒3n=36⇒ {3}^{n} = {3}^{6}

⇒n=6⇒ n = 6

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