If the inter-quartile range is the distance between the first and third quartiles, then the inter-decile range is the distance between the first and ninth decile. (Deciles divide a distribution into ten equal parts.) If IQ is normally distributed with a mean of 100 and a standard deviation of 16, what is the inter-decile range of IQ?
z score for first decile, i.e. 10th percentile is -1.282 and for ninth decile, z score= 1.282
You can use excel function NORMSINV(area) to find these z score
1st decile z score = NORMSINV(0.10) = -1.282 and 9th decile = NORMSINV(0.90) = 1.282
We have mean = 100 and standard deviation is 16
Using z score formula, assuming that x is 1st decile value
and
9th decile calculation
Therefore, Inter decile range = 120.5 - 79.5 = 41
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