The mean of the values of 1,2,3.n with respective frequencies x, 2x, 3x,.nx is?

Question

Answer

Mean of the values of 1,2,3.n with respective frequencies x, 2x, 3x,.nx

Let's first understand some basic concepts before solving the problem:

Mean

Mean is also known as the arithmetic average. It is calculated by adding up all the values in a set of data and dividing the sum by the total number of values.

Mathematically, Mean is represented as:

Mean = (Sum of all values) / (Total number of values)

Frequency

Frequency is the number of times an event occurs in a set of data. It is represented by 'f'. In this problem, we have given frequencies as x, 2x, 3x, and nx.

Weighted Mean

Weighted mean is the average of a set of data where each value in the data set is multiplied by a weight factor. In this problem, we have to find the weighted mean of values 1, 2, 3, n with respective frequencies x, 2x, 3x, and nx.

Mathematically, Weighted Mean is represented as:

Weighted Mean = (Sum of (Value * Frequency)) / (Total Frequency)

Solution

Now, we can use the formula of weighted mean to solve this problem. Let's substitute the given values:

Weighted Mean = [(1 * x) + (2 * 2x) + (3 * 3x) + (n * nx)] / (x + 2x + 3x + nx)

Simplifying the above expression:

Weighted Mean = [(x + 4x + 9x + n^2x)] / (6x + nx)

Weighted Mean = [(14x + n^2x)] / (6x + nx)

Weighted Mean = (x(14 + n^2)) / (x(6 + n))

Weighted Mean = (14 + n^2) / (6 + n)

Therefore, the mean of the values of 1, 2, 3, n with respective frequencies x, 2x, 3x, and nx is (14 + n^2) / (6 + n).

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