Certainly! Let's go through the problem step by step to understand how to find the deleted number.
1. Understand Given Information:
- The mean of 6 numbers is 20.
- When one number is deleted, the mean of the remaining 5 numbers is 15.
2. Calculate the Total Sum of the 6 Numbers:
- The mean is the sum of the numbers divided by the quantity of those numbers.
- Let the total sum of the 6 numbers be [tex]\( S \)[/tex].
- The mean of the 6 numbers is 20, so:
[tex]\[
\frac{S}{6} = 20
\][/tex]
- Solve for [tex]\( S \)[/tex]:
[tex]\[
S = 20 \times 6 = 120
\][/tex]
3. Calculate the Total Sum of the Remaining 5 Numbers:
- After deleting one number, the mean of the remaining 5 numbers is 15.
- Let the total sum of the remaining 5 numbers be [tex]\( S' \)[/tex].
- The mean of these 5 numbers is 15, so:
[tex]\[
\frac{S'}{5} = 15
\][/tex]
- Solve for [tex]\( S' \)[/tex]:
[tex]\[
S' = 15 \times 5 = 75
\][/tex]
4. Determine the Deleted Number:
- The deleted number is the difference between the total sum of the 6 numbers and the total sum of the remaining 5 numbers.
- Let the deleted number be [tex]\( d \)[/tex]:
[tex]\[
d = S - S'
\][/tex]
- Substitute the values we found:
[tex]\[
d = 120 - 75 = 45
\][/tex]
Therefore, the deleted number is 45.
