The following data give the annual salaries in thousand...

The following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers. 50 72 57 37 46 64 36 51 35 62 75 40 68 45 76 61 58 54 64 59 a. Calculate the values of the three quartiles and the interquartile range. $$Q_1 =$$ $$Q_2 =$$ $$Q_3 =$$ $$IQR =$$ b. Find the approximate value of the 20th percentile.

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00:01 Hey there, welcome to numerate.

00:03 So we're giving a list of values over here in a data set of 20 randomly selected healthcare workers and their annual salaries.

00:10 So for part a, we're asked to find the quartiles here.

00:14 And for each of the quartiles, we're going to use the percentile rank method in order to find each one.

00:20 It's a percentile rank of quartile one, which is the 25th percentile, which is equivalent to one -fourth times n plus one, where n is our sample size.

00:30 In this case, we have 20 plus 1.

00:34 This gives us a value of 21 divided by 4, which is equivalent to around 55 .25.

00:42 So it's basically a 5 .2 fifth term.

00:47 And if we rearrange our values from these two greatest, we can use the 5 point between the 5th and 6th term is our quartile 1.

00:58 So what we have here for our quartile 1 is equivalent as 46.

01:08 For our quartile 2, aka the median, the percentile rank equation is going to be percentile rank equals that's going to be one half times 21 because we know we're now 20 plus 1 equals 21.

01:28 21 divided by 2 equals 10 .5.

01:34 So it's going to be 10 .5.

01:36 Term corresponding to a quartile 2 of around 56 .5.

01:44 For quartile 3, percentile rank equation, 75th percentile, which is the quartile 3...

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