Statistics question...IQR!!!?

alvinchou2003

2008-08-18 8:34 pm

48. IQ, finis. Consider the IQ model N (100, 16) one last time.

a) What IQ represents the 15th percentile? invNorm (0.15, 100, 16) = 83.42

b) What IQ represents the 98th percentile? invNorm (0.98, 100, 16) = 132.86

c) What’s the IQR of the IQs? I dont know this one. How can I compute IQR?

更新1:

75th percentile = mean + 0.6745*standard deviation 25th percentile = mean - 0.6745*standard deviation what is the mean and SD?

更新2:

oh...i get it... but why is 0.6745?

回答 (1)

[匿名]

2008-08-18 8:42 pm

✔ 最佳答案

IQR = Inter Quartile Range = Upper Quartile - Lower Quartile.

UQ = 75th percentile
LQ = 25th percentile.

For a normal distribution
75th percentile = mean + 0.6745*standard deviation
25th percentile = mean - 0.6745*standard deviation

So in this case IQR of IQs is 110.79 - 89.21 = 21.58

By the way, your description of the distribution as N(100, 16) should be N(100, 16^2). Normal distributions are always quoted as N(mean, variance) or N(mean, s.d. ^2).

Edit. Mean = 100 and s.d. = 16 come from the specification of the normal distribution.

The 0.6745 comes from tables of the standard normal distribution with mean = 0 and s.d. = 1.

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