The average height of a group of students was 134.4 cm.When Mr Lim measured and recorded the height of these students, he wronglyrecorded one student's height as 193 cm when it should have been 139 cm.As a result, Mr Lim calculated the average height as 143.4 cm.How many students were there in the group?
Question
The average height of a group of students was 134.4 cm.When Mr Lim measured and recorded the height of these students, he wronglyrecorded one student's height as 193 cm when it should have been 139 cm.As a result, Mr Lim calculated the average height as 143.4 cm.How many students were there in the group?
Solution
Step 1: First, we need to find out the total height that Mr. Lim calculated. We do this by multiplying the average height he calculated (143.4 cm) by the number of students. But we don't know the number of students yet, so let's call it 'x'. So, the total height according to Mr. Lim is 143.4x.
Step 2: We also know the total height should have been less because one student's height was recorded more than it should have been. The student's height was recorded as 193 cm but should have been 139 cm. So, the difference is 193 - 139 = 54 cm.
Step 3: Therefore, the correct total height should have been 143.4x - 54.
Step 4: We also know that the correct average height should have been 134.4 cm. The average is calculated by dividing the total height by the number of students. So, the correct total height is also 134.4x.
Step 5: Now we can set up the equation 143.4x - 54 = 134.4x and solve for x.
Step 6: If we subtract 134.4x from both sides, we get 9x = 54.
Step 7: Finally, if we divide both sides by 9, we get x = 6.
So, there were 6 students in the group.
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