The average of $5, 0, 6, \frac{1}{4}$ and $8 \frac{3}{4}$ is
Average Calculation for Given Numbers
The average (or mean) is calculated by summing all the numbers in a set and then dividing by the count of numbers in that set.
Step-by-step Solution
The numbers provided are $5, 0, 6, \frac{1}{4}$, and $8 \frac{3}{4}$.
- First, convert the mixed number $8 \frac{3}{4}$ into an improper fraction. $8 \frac{3}{4} = \frac{(8 \times 4) + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4}$.
- Next, calculate the sum of all the numbers: $5, 0, 6, \frac{1}{4}, \frac{35}{4}$. Sum $= 5 + 0 + 6 + \frac{1}{4} + \frac{35}{4}$ Combine the whole numbers: $5 + 0 + 6 = 11$. Combine the fractions: $\frac{1}{4} + \frac{35}{4} = \frac{1 + 35}{4} = \frac{36}{4}$. Simplify the fraction sum: $\frac{36}{4} = 9$. Add the results: Sum $= 11 + 9 = 20$.
- Count the total number of values. There are 5 numbers.
- Finally, calculate the average using the formula: Average $= \frac{\text{Sum of numbers}}{\text{Count of numbers}}$. Average $= \frac{20}{5}$ Average $= 4$.
Thus, the average of the given numbers is 4.
Important Questions from Average
The average salary of employees of a factory is ₹15,000. The average salary of 250 of the employees is ₹16,000 and that of the remaining employees is ₹13,750. Total number of employees in the factory is:
Find the mean of prime numbers between 1 and 30.
If mode and mean of a data are 18 and 21 respectively, then median of the data is
The average of the numbers 5, 3, 9, 11, 29 and (p+1) is 12. The average increases by 2 when the numbers (q – 5) and (q +11) are also included. Find the value of q.
In a particular week, the average earning per day of a plumber from Monday to Wednesday remained ₹580 and from Thursday to Saturday it was ₹612. If the average earning for the whole week was ₹675, then how much did he earn on Sunday?
