Question

In: Statistics and Probability

Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8,576 1,401 1,910 9,057 2,508...

Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.

8,576	1,401	1,910	9,057	2,508	11,641
621	14,138	6,581	1,887	2,874	1,383
10,708	7,628	4,100	4,428	754	2,170
3,726	5,910	8,472

compute the lower and upper limits (to 2 decimals). If required enter negative value as negative number.

Lower limit____

Upper limit____

Does the data contain any outliers?

Solutions

Expert Solution

first arrange the data in ascending order

621
754
1383
1401
1887
1910
2170
2508
2874
3726
4100
4428
5910
6581
7628
8472
8576
9057
10708
11641
14138

Now, divide the data sets into two equal parts, i.e. bottom 10 data values on one side and top 10 data values on other side

Lower half is

621
754
1383
1401
1887
1910
2170
2508
2874
3726

First quartile = median of lower half = halfway between two middle values

two middles values are 1887 and 1910

So, First quartile = (1887+1910)/2 = 1898.5 = Q1

Upper half is

4428
5910
6581
7628
8472
8576
9057
10708
11641
14138

Third quartile = median of upper half = halfway between two middle values

two middles values are 8472 and 8576

So, third quartile = (8472+8576)/2 = 8524 = Q3

Interquartile range or IQR = Q3 - Q1 = 8524 - 1898.5 = 6625.5

Lower limit of data set = Q1- 1.5*IQR

= 1898.5- (1.5*6625.5)

= 1898.5 - 9938.25

= -8039.75

Upper limit of data set = Q3+ 1.5*IQR

= 8524+(1.5*6625.5)

= 8524 + 9938.25

= 18462.25

No, there is no outlier because none of the data set is outside the range (-8039.75, 18462.25)

orchestra answered 1 year ago

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