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
If the average weight of 10 students is 25 kg and that of another 10 students is 35 kg, then the average weight of these 20 students is:
The average of 5 numbers is 15. Find a number which should be included in these numbers to make the average 16.
If the mean of the numbers 2, (p + 1), 8, 19, 16, 3 and p is 9, then find the mode of the numbers.
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?
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.
