Arithmetic Mean

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

Given Information

- The arithmetic mean of the series is 60.
- Four values are known: 10, 25, 30, and 35.

Calculating the Missing Value

To find the missing fifth value, we can use the formula for the arithmetic mean and the given information.

Step 1: Find the sum of the known values.
- Sum = 10 + 25 + 30 + 35 = 100

Step 2: Find the total number of values in the series.
- Total number of values = 4 (known values) + 1 (missing value) = 5

Step 3: Use the formula for the arithmetic mean to find the sum of all values.
- Sum = Mean × Total number of values
- 100 = 60 × 5

Step 4: Solve for the missing value.
- 100 = 60 × 5
- Divide both sides of the equation by 60:
- 100 ÷ 60 = 5
- 1.67 = 5

Therefore, the missing fifth value of the series is 1.67.

Conclusion

The missing fifth value of the series is 1.67. This was calculated by finding the sum of the known values, determining the total number of values in the series, using the formula for the arithmetic mean to find the sum of all values, and solving for the missing value.