Statistics
Statistics
nta_abhyas_2025
Grade 11
Question:
A number equal to 2 times the mean and with a frequency equal to $k$ is inserted in a data having $n$ observations. If the new mean is $\frac{7}{4}$ times the old mean, then the value of $\frac{k}{n}$ is
Step-by-Step Solution
Key Concept: The mean of even-positioned values in an arithmetic sequence can be expressed in terms of the sequence parameters.
Given $x_{\text{even}} = \frac{4}{9}$, from the information $x_{\text{even}} = \frac{4k+a}{2k} = \frac{4}{9}$. Setting up the equation $9(4k+a) = 8k$ gives $3n + 6k = 4n + 4k$, which simplifies to $2k = n$. Therefore $\frac{k}{n} = 0.5$.
Correct Answer: 0.5