The average height of 35 boys in a class was calculated as 180cm. It has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm. Find the actual average height of the boys in the class (Round off your answer to two decimal places)?
Correct answer: B. 178.29 cm
- A. 179.29 cm
- B. 178.29 cm
- C. 179.38 cm
- D. 178.39 cm
Explanation
The recorded total was 35 boys × 180 centimetres = 6300 centimetres. The incorrect height of 166 centimetres must be replaced by 106 centimetres, reducing the total by 60 centimetres to 6240 centimetres. The actual average is 6240 centimetres / 35 boys = 178.2857 centimetres, which rounds to 178.29 centimetres. The likely mistake is adding 60 centimetres instead of subtracting it.
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About Averages
An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.
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