Arithmetic Mean (AM)

The arithmetic mean, also known as the average, is a measure of central tendency that represents the typical or average value of a set of numbers. It is calculated by summing up all the values in the set and dividing the sum by the total number of values.

To find the arithmetic mean of the given set of values (1, 2, 3.5) with frequencies (1, 2, 3.5), we need to follow these steps:

Step 1: Calculate the product of each value and its corresponding frequency

To calculate the product of each value and its corresponding frequency, we multiply each value by its frequency.

The product for the first value (1) with a frequency of 1 is 1 * 1 = 1.
The product for the second value (2) with a frequency of 2 is 2 * 2 = 4.
The product for the third value (3.5) with a frequency of 3.5 is 3.5 * 3.5 = 12.25.

Step 2: Sum up all the products

Next, we sum up all the products calculated in the previous step.

Sum of products = 1 + 4 + 12.25 = 17.25

Step 3: Calculate the sum of frequencies

We need to calculate the sum of frequencies, which is the total number of values in the set.

Sum of frequencies = 1 + 2 + 3.5 = 6.5

Step 4: Divide the sum of products by the sum of frequencies

Finally, we divide the sum of products by the sum of frequencies to find the arithmetic mean.

Arithmetic mean (AM) = Sum of products / Sum of frequencies
AM = 17.25 / 6.5
AM ≈ 2.65

Therefore, the arithmetic mean of the given set of values (1, 2, 3.5) with frequencies (1, 2, 3.5) is approximately 2.65.

In summary, the arithmetic mean represents the average value of a set of numbers. To find the arithmetic mean, we multiply each value by its corresponding frequency, sum up all the products, and divide the sum by the total number of values. Applying this process to the given set of values and frequencies, we find that the arithmetic mean is approximately 2.65.