The average marks of 14 students was 71. It was later found that the marks of one of the students has been wrongly entered as 42 instead of 56 and of another as 74 instead of 32. What is the correct average?
Average age of seven persons in a group is 30 years, the average age of five persons of this group is 31 years. What is the average age of the other two persons in the group?
Pls help***
The average marks of 14 students was 71.
This mean : ( x1 + x2 + x3 + ... x14 ) / 14 = 71
( x1 + x2 + x3 + ... x14 ) / 14 = 71 Multiply both sides by 14
x1 + x2 + x3 + ... x14 = 71 * 14
x1 + x2 + x3 + ... x14 = 994 = Total marks
On this marks you must add 56 - 42 = 14 and subtract 74 - 32 = 42
New marks = 994 + 14 - 42 = 966
The correct average = 966 / 14 = 69
Average age of seven persons in a group is 30 years.
This mean : ( x1 + x2 + x3 + x4 + x5 + x6 + x7 ) / 7 = 30
( x1 + x2 + x3 + x4 + x5 + x6 + x7 ) / 7 = 30 Multiply both sides by 7
x1 + x2 + x3 + x4 + x5 + x6 + x7 = 30 * 7
x1 + x2 + x3 + x4 + x5 + x6 + x7 = 210
The average age of five persons of this group is 31 years.
This mean : ( x1 + x2 + x3 + x4 + x5 ) / 5 = 31
( x1 + x2 + x3 + x4 + x5 ) / 5 = 31 Multiply both sides by 5
x1 + x2 + x3 + x4 + x5 = 31 * 5
x1 + x2 + x3 + x4 + x5 = 155
Sum of the age of other two persons = ( x1 + x2 + x3 + x4 + x5 + x6 + x7 ) - ( x1 + x2 + x3 + x4 + x5 ) = x6 + x7 = 210 - 155 = 55
The average age of the other two persons = 55 / 2 = 27.5 years
To find the correct average in the first question, we need to calculate the sum of the original marks and divide it by the number of students. Here are the steps:
1. Calculate the sum of the original marks by multiplying the average (71) by the number of students (14). Sum = 71 * 14 = 994.
2. Find the sum of the wrong marks that need to be corrected. The sum of the wrong marks is 42 + 74 = 116.
3. Subtract the sum of the wrong marks from the original sum: Corrected Sum = Original Sum - Sum of Wrong Marks = 994 - 116 = 878.
4. Correct the two wrong marks: Subtract the wrong marks from the corrected sum and add the correct marks: 878 - 42 + 56 - 74 + 32 = 850.
5. Finally, divide the corrected sum by the number of students to get the correct average: Correct Average = Corrected Sum / Number of Students = 850 / 14 ≈ 60.71.
Therefore, the correct average marks of the students is approximately 60.71.
For the second question, we can use the concept of weighted averages to find the average age of the two remaining persons. Here's how to do it:
1. Multiply the average age of the entire group (30) by the total number of persons (7) to find the total age of the group: Total Age = Average Age * Number of Persons = 30 * 7 = 210.
2. Multiply the average age of the five persons (31) by their total number (5) to find their total age: Total Age of Five Persons = Average Age of Five Persons * Number of Persons = 31 * 5 = 155.
3. Subtract the total age of the five persons from the total age of the group to find the total age of the two remaining persons: Total Age of Two Persons = Total Age - Total Age of Five Persons = 210 - 155 = 55.
4. Finally, divide the total age of the two remaining persons by their total number (2) to find their average age: Average Age of Two Persons = Total Age of Two Persons / Number of Persons = 55 / 2 = 27.5.
Therefore, the average age of the two remaining persons in the group is 27.5 years.