Question

How much oil wells in a given field will ultimately produce is crucial information in deciding

Answer 1

The five number summary of the data is given below :

• Maximum = 157
• Minimum = 3
• Median = 47
• Lower quartile = 34
• Upper quartile = 65.5

• 157 is an outlier .

The data given  :

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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