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The average height of 15 students is calculated as 75. But later it was found that the height of 1 student wrongly entered as 35 instead of 38 and another as 46 instead of 63.The correct average is
- a)71
- b)73
- c)75
- d)76
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The average height of 15 students is calculated as 75. But later it wa...
{(15*75)-(35+46)+(38+63)} / 15 = (1125 – 81 + 101) / 15
= 1145/15 = 76.33 = 76
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The average height of 15 students is calculated as 75. But later it wa...
Given:
- Average height of 15 students is calculated as 75.
- One student's height was wrongly entered as 35 instead of 38.
- Another student's height was wrongly entered as 46 instead of 63.
To find:
The correct average height.
Solution:
Step 1: Calculate the sum of the heights before correction:
- The average height of 15 students is calculated as 75. Therefore, the sum of the heights before correction is 15 * 75 = 1125.
Step 2: Find the difference between the incorrect and correct heights:
- For the first student, the height was wrongly entered as 35 instead of 38. So, the difference is 38 - 35 = 3.
- For the second student, the height was wrongly entered as 46 instead of 63. So, the difference is 63 - 46 = 17.
Step 3: Adjust the sum of heights by adding the differences:
- Subtract the difference of the first student's height from the sum: 1125 - 3 = 1122.
- Subtract the difference of the second student's height from the sum: 1122 - 17 = 1105.
Step 4: Calculate the correct average height:
- Divide the adjusted sum by the total number of students (15): 1105 / 15 = 73.67 (rounded to 2 decimal places).
Conclusion:
The correct average height of the 15 students is 73.67, which is closest to option 'D' (76).
- Average height of 15 students is calculated as 75.
- One student's height was wrongly entered as 35 instead of 38.
- Another student's height was wrongly entered as 46 instead of 63.
To find:
The correct average height.
Solution:
Step 1: Calculate the sum of the heights before correction:
- The average height of 15 students is calculated as 75. Therefore, the sum of the heights before correction is 15 * 75 = 1125.
Step 2: Find the difference between the incorrect and correct heights:
- For the first student, the height was wrongly entered as 35 instead of 38. So, the difference is 38 - 35 = 3.
- For the second student, the height was wrongly entered as 46 instead of 63. So, the difference is 63 - 46 = 17.
Step 3: Adjust the sum of heights by adding the differences:
- Subtract the difference of the first student's height from the sum: 1125 - 3 = 1122.
- Subtract the difference of the second student's height from the sum: 1122 - 17 = 1105.
Step 4: Calculate the correct average height:
- Divide the adjusted sum by the total number of students (15): 1105 / 15 = 73.67 (rounded to 2 decimal places).
Conclusion:
The correct average height of the 15 students is 73.67, which is closest to option 'D' (76).
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The average height of 15 students is calculated as 75. But later it was found that the height of 1 student wrongly entered as 35 instead of 38 and another as 46 instead of 63.The correct average isa)71b)73c)75d)76Correct answer is option 'D'. Can you explain this answer?
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