How do you find the interquartile range?

How can you find the interquartile range only knowing the mean, standard deviation, n that its normal? (STATs)?

• for example: scores on the American College Tests (ACT) are normally distributed with a mean of 18 and a standard deviation of 6. the interquartile range of the scores is approximately: ???????/ Answer is 8.1 but why????? please explain

• Answer:

  The IQR is the difference between the 1st quartile and the 3rd quartile (or the 25th percentile and the 75th percentile), thus, if we can find the 25th and 75th percentiles, we can then find the IQR. From a standard normal distribution table (or calculator), the 75th percentile has a z-score of 0.674. We can use this to find the actual 75th percentile of the distribution: z-score = (x - mean)/(st. dev) 0.674 = (x - 18)/6 4.044 = x - 18 (multiplying both sides by 6) 22.044 = x (adding 18 to both sides) Because of the symmetry of the standard normal distribution, the 25th percentile is the same distance from the mean as the 75th percentile is, but on the other side. Thus, the 25th percentile can be found by: 25th = 18 - 4.044 25th = 13.956 Thus, the interquartile range is: 22.044 - 13.956 = 8.088 or approximately 8.1