6:12 Question Question 10 An outlier in a graph of data defined as an individual

Question

6:12 Question Question 10 An outlier in a graph of data defined as an individual data point that falls outside the overall pattern of the graph. There are several rules thumb use a) the assumption of normality and the rule using three population standard deviations and b) the quartiles and interquartile range. Calculated the following criteria for the test grade data set (full credit 40) as follows: 16, 16, 17, 19, 23, 24, 25, 37, 38, 39 What is interquartile range of the data? A 18 B 19 C 20 D 21

Explanation / Answer

IQR = Q3 - Q1 .

Now, Q2 or the median is the middlemost observation of the sorted dataset.

Q2 divides the observations into two sets, left and right.  

The middlemost observation of the left part is Q1 and middlemost observation of the Right part is Q3.

Here no of observation is 10 (even) .

So, somewhere between 5th and 6th will be the middlemost value, we take an average of the 5th and 6th value. Here 23.5 .

Now, below 5th obseravtion, there are 4 observation, of which middlemost is somewhere between 2nd and 3rd. Taking average, we havehere Q1 as 16.5

Similarly Q3 as 37.5

So, IQR = 37.5-16.5 = 21 . So option D is correct.

This s the thumbrule to get Quartiles. if you need mathematical expressions, let me know below, I will provide you with the same. Thanks

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