The median height of 1240 students in a school is 142 centimeres. The distributiim of the students heights is approximately symmetrical, and 248 of the students are more than 147 centimeters tall. What approximate percentile is represented by a height o f 137 centimeters?
Please Explain with detail.
If the distribution is symmetrical, then the mean = median = 142
248 students are taller than 247 cm
The percent of students taller than 247 = \frac{248}{1240} * 100 = 20%
This means that someone who is 247 cm is taller than 80% of the school
247 = 80th percentile
The 80th percentile is also 105 (247 - 142) cm away from the mean
Again as the graph is symmetrical, 20th percentile would be 105cm away from the mean as well
20th percentile = 142 - 105 = 37
The question is asking for percentile of 137 cm
Which lies in between 37 and 142, so the answer would be b/w 20 and 50
And will probably be a lot closer to 50 than 20 (because 137 is a lot closer to 142 than 37)
So, then answer will be something like 45th percentile
(Depending on the options)
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What about if it is 147 instead of 247 cm tall?
mean = median = 142
147 = 80th percentile
The 80th percentile is 5 (147 - 142) cm away from the mean
Again as the graph is symmetrical, 20th percentile would be 5cm away from the mean as well
20th percentile = 142 - 5 = 137
Ans. 20th percentile
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