Question

  Percentile

Mean 1st 5th 19th 25th 50th 75th 90th 95th 99th

122.2    39 55 65 85 114 150 190 217 278

Use the 5th, 50th and 95th percentiles of this distribution to estimate the mean and standard deviation of this distribution assuming that the distribution is Normal. Explain your method for doing this.

Answer 1

Assuming the population distribution is normal,

For normal distribution, mean = median = 50^th percentile = 114

Moreover, we can write

5^th percentile where denotes the population standard deviation.

and 95^th percentile

So,

ans-> mean = 114 and standard deviation = 35.87