5. Use the accompanying data set to complete the following actions a. Find the q

Question

5. Use the accompanying data set to complete the following actions a. Find the quartiles. b. Find the interquartile range. c. Identify any outliers. 59 62 57 59 61 54 60 62 59 58 62 64 63 65 72 a. Find the quartiles. The first quartile, Q1, is The second quartile, Q2, is The third quartile, Q3, is (Type integers or decimals.) b. Find the interquartile range. The interquartile range (IQR) is Type an integer or a decimal.) c. Identify any outliers. Choose the correct answer below. 0 A. There exists at least one outlier in the data set at (Use a comma to separate answers as needed.) Bt There are no outliers in the data set.

Explanation / Answer

5.

The data sequence is 59 62 57 59 61 54 60 62 59 58 62 64 63 65 72

If we sort the sequence in increasing order it will be

54 57 58 59 59 59 60 61 62 62 62 63 64 65 72 . Number of elements= 15 so the middle term or median will be (15+1)/2=8 th term=61 (indicaated in bold)

so Q2 is 61

Now the lower half of the data is the points lie left of Q2= 54 57 58 59 59 59 60 which has length 7. so the middle point of this subsequence= (7+1)/2 th term= 4th term=59

so the Q1 is 59

The upper half of the data is the point lie right of Q2=62 62 62 63 64 65 72. The middle point of this subsequence will be (7+1)/2=4th term=63.

So Q3 is 63

so,

a. Finding Quartiles.....

Q1=59, Q2=61, Q3=63

b. Finding IQR......

IQR= Q3-Q1=63-59=4

C. Finding Outliers.

Any values which are much beyond from IQR can be considered outlier.

The formula for the same is any values which does not lie between [Q1-t*IQR,Q3+t*IQR] can be considered an outlier. If we consider t=1.5 (conventional value) then the range become [59-1.5*4, 63+1.5*4]=[59-6 , 63+6]=[53,69]

So the data points which lies beyond that i.e data points which are either less than 53 or greater than 69 can be considered as outlier.

So the outlier is 72

So option A is correct

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