Given, mean = (3 median - mode) * k

We need to find the value of k.

Explanation:

Mean, median and mode are measures of central tendency used in statistics.

Mean: It is the average of a set of numbers. It is calculated by adding up all the numbers in the set and dividing the sum by the total number of values.

Median: It is the middle value of a set of numbers. If there are an odd number of values, the median is the middle value. If there are an even number of values, the median is the average of the two middle values.

Mode: It is the value that appears most frequently in a set of numbers. A set of numbers can have more than one mode or no mode at all.

Now, we have the formula:

mean = (3 median - mode) * k

We can rearrange this formula to get the value of k as:

k = mean / (3 median - mode)

Therefore, to find the value of k, we need to know the values of mean, median and mode.

We can use the following steps:

Step 1: Find the median of the set of numbers.

Step 2: Find the mode of the set of numbers.

Step 3: Find the mean of the set of numbers.

Step 4: Substitute the values of mean, median and mode in the formula.

Step 5: Simplify the expression to get the value of k.

Let's consider an example to understand this concept better.

Example:

Find the value of k if the mean, median and mode of the set of numbers {2, 3, 4, 4, 5, 6, 7} are given.

Step 1: Find the median of the set of numbers.

The median is the middle value of the set of numbers.

Arrange the set of numbers in ascending order: {2, 3, 4, 4, 5, 6, 7}

The middle value is 4.

Therefore, the median of the set of numbers is 4.

Step 2: Find the mode of the set of numbers.

The mode is the value that appears most frequently in the set of numbers.

In this set of numbers, 4 appears twice, which is more than any other value.

Therefore, the mode of the set of numbers is 4.

Step 3: Find the mean of the set of numbers.

The mean is the average of the set of numbers.

Add up all the numbers in the set: 2 + 3 + 4 + 4 + 5 + 6 + 7 = 31

Divide the sum by the total number of values: 31 / 7 = 4.43 (rounded to two decimal places)

Therefore, the mean of the set of numbers is 4.43.

Step 4: Substitute the values of mean, median and mode in the formula.

mean = 4.43, median = 4, mode = 4

k = mean / (3 median - mode)

k = 4.43 / (3 * 4 - 4)

k = 4.43 / 8

k = 0.55375 (rounded to five decimal places)

Step 5: Simplify the expression to get the value of k.

Therefore, the value of k is 0.55375 or 1/

By empirical formula
mode = 3median - 2 mean
it is given that,
mean = (3median - mode).k
if we put value ofnk as 1/2
mean = 3/2 median - mode/2
mean = (3median - mode)/2 ....taking lcm
2mean = 3median - mode
mode = 3 median - 2 mean