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Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is
- a)48
- b)49
- c)50
- d)60
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Mean of 100 items is 49. It was discovered that three items which shou...
Sum of 100 observations = 100 x 49 = 4900
Correct sum = 4900 - [40 + 20 + 50] + [60 + 70 + 80] = 5000
∴ Correct mean = 5000/100 = 50
Correct sum = 4900 - [40 + 20 + 50] + [60 + 70 + 80] = 5000
∴ Correct mean = 5000/100 = 50
Most Upvoted Answer
Mean of 100 items is 49. It was discovered that three items which shou...
Given---
Number of Items(n) =100
Mean of these items(∑)= 49
Using the Formula,
Mean(∑) = Sum of all items/ Number of Items
∑ = ∑x ÷ n
Thus, ∑x = ∑ × n
∑x = 49 × 100
∑x = 4900
Sum of all items = 4900
or
Incorrect Value of ∑x = 4900
Sum of the Correct Values of the Items = 60 + 70 + 80
= 210
Sum of the Values which is incorrectly noticed = 40 + 20 +50
= 110
The difference in the values = Correct Value - Incorrect Value
= 210 -110
= 100
Thus, the 100 should be added to the incorrect ∑x for obtaining the correct value of ∑x.
Thus, New ∑x = 4900 + 100
= 5000
Again Using the Formula,
Correct Mean = New ∑x ÷ n
= 5000 ÷ 100
= 50
Thus, the Correct Mean is 50.
Number of Items(n) =100
Mean of these items(∑)= 49
Using the Formula,
Mean(∑) = Sum of all items/ Number of Items
∑ = ∑x ÷ n
Thus, ∑x = ∑ × n
∑x = 49 × 100
∑x = 4900
Sum of all items = 4900
or
Incorrect Value of ∑x = 4900
Sum of the Correct Values of the Items = 60 + 70 + 80
= 210
Sum of the Values which is incorrectly noticed = 40 + 20 +50
= 110
The difference in the values = Correct Value - Incorrect Value
= 210 -110
= 100
Thus, the 100 should be added to the incorrect ∑x for obtaining the correct value of ∑x.
Thus, New ∑x = 4900 + 100
= 5000
Again Using the Formula,
Correct Mean = New ∑x ÷ n
= 5000 ÷ 100
= 50
Thus, the Correct Mean is 50.
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Community Answer
Mean of 100 items is 49. It was discovered that three items which shou...
**Given information:**
- The mean of 100 items is 49.
- Three items were wrongly read as 40, 20, and 50 instead of their correct values of 60, 70, and 80.
**To find:**
- The correct mean of the 100 items.
**Solution:**
To find the correct mean, we need to calculate the sum of the correct values of the 100 items and divide it by 100.
Let's calculate the sum of the correct values of the 100 items first.
Sum of the correct values = (Sum of the wrong values + Sum of the differences)
Now, let's calculate the sum of the wrong values:
Sum of the wrong values = 40 + 20 + 50 = 110
Next, let's calculate the sum of the differences:
Sum of the differences = (60 - 40) + (70 - 20) + (80 - 50) = 20 + 50 + 30 = 100
Therefore, the sum of the correct values = Sum of the wrong values + Sum of the differences = 110 + 100 = 210
Now, we can calculate the correct mean:
Correct mean = Sum of the correct values / Number of items = 210 / 100 = 2.1
However, since the given mean is 49, it means that the sum of the 100 items is 100 * 49 = 4900.
Therefore, the sum of the correct values should also be 4900.
Let's calculate the correct mean again using this sum:
Correct mean = Sum of the correct values / Number of items = 4900 / 100 = 49
Hence, the correct mean of the 100 items is 49, which corresponds to option C.
- The mean of 100 items is 49.
- Three items were wrongly read as 40, 20, and 50 instead of their correct values of 60, 70, and 80.
**To find:**
- The correct mean of the 100 items.
**Solution:**
To find the correct mean, we need to calculate the sum of the correct values of the 100 items and divide it by 100.
Let's calculate the sum of the correct values of the 100 items first.
Sum of the correct values = (Sum of the wrong values + Sum of the differences)
Now, let's calculate the sum of the wrong values:
Sum of the wrong values = 40 + 20 + 50 = 110
Next, let's calculate the sum of the differences:
Sum of the differences = (60 - 40) + (70 - 20) + (80 - 50) = 20 + 50 + 30 = 100
Therefore, the sum of the correct values = Sum of the wrong values + Sum of the differences = 110 + 100 = 210
Now, we can calculate the correct mean:
Correct mean = Sum of the correct values / Number of items = 210 / 100 = 2.1
However, since the given mean is 49, it means that the sum of the 100 items is 100 * 49 = 4900.
Therefore, the sum of the correct values should also be 4900.
Let's calculate the correct mean again using this sum:
Correct mean = Sum of the correct values / Number of items = 4900 / 100 = 49
Hence, the correct mean of the 100 items is 49, which corresponds to option C.
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Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80were wrongly read as 40, 20, 50 respectively. The correct mean isa)48b)49c)50d)60Correct answer is option 'C'. Can you explain this answer?
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