How much oil wells in a given field will ultimately produce is crucial information in deciding
whether to drill more wells. Here are the estimated total amounts of oil recovered from 38 wells in
the Devonian Richmond Dolomite area of the Michigan basin, in thousands of barrels. The data is
provided in ascending order, along with a dotplot.
92
98
3
13
15
19
21
22
25
31
33
35
35
35
37
37
38
43
43
45
46
48
49
50
50
53
56
57
59
63
65
66
70
70
74
80
82
157
.
.
0
25
150
.
50
75
100
125
Total Oil Recovered (thousands of barrrels)
I is an outlier because it is greater than

3, 13, 15, 19, 21, 22, 25, 31, 33, 35, 35, 35, 37, 37, 38, 43, 43, 45, 46, 48, 49, 50, 50, 53, 56, 57, 59, 63, 65, 66, 70, 70, 74, 80, 82, 92, 98, 157

The five number summary for the data include ;

Maximum = 157

Minimum = 3

Median(Q2) = 1/2(n+1)th term

n = number of terms = 38

Q2 = 1/2(n+1)th term

Q2 = 1/2(39)th term = 19.5th term = (46+48)/2 = 47

Upper quartile (Q3) = 3/4(n+1)th term

Q3 = 3/4(39)th term = 29.25th term = (65+66)/2 = 65.5

Lower quartile (Q1) = 1/4(n+1)th term

Q1 = 1/4(39)th term = 9.75th term = (33+35)/2 = 34

Outliers :

Lower limit = Q1 - (1.5 × IQR)

IQR = Q3 - Q1 = (65.5 - 34) = 31.5

Lower outlier = 34 - (1.5 × 31.5) = - 13.25

Upper limit = Q3 + (1.5 × IQR)

Upper limit = 65.5 + (1.5 × 31.5) = 112.75

Outliers are values below or above the the lower limit or values above the upper limit.

157 falls above the upper limit, hence, 157 is an outlier. .

The boxplot of the data is attached below.

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