Question

(b) The five number summary for the number of circuits for those describing the high-quality site is (0, 7.5, 80, 122.5, 440), while the five number summary for those describing the low-quality site is (0, 0, 0, 42.5, 185). Use the IQR method to identify any outliers in either group. Justify your answer.

Answer 1

(i) Outlier is present

(ii) Outlier is not present.

Explanation:

The outlier is said to be present in data if:

The minimum number then Q₁ - 1.5 × IQR

and maximum number then 1.5 × IQR - Q₃

is present in data.

(i) For high quality site we have five number summary is: (0, 7.5, 80, 122.5, 440)

Thus, Minimum Value = 0

First Quartile(Q₁) = 7.5

Median = 80

Third Quartile(Q₃) = 122.5

Maximum Value = 440

Thus, IQR = Q₃ - Q₁ = 115

then, Q₁ - 1.5 × IQR = -165

and, 1.5 × IQR + Q₃ = 295

Since, the minimum value and maximum value is 0 and 440 respectively thus, 440 is larger than 295.

Hence, Outlier is present in this data.

(ii) For low quality site we have five number summary is: (0, 0, 0, 42.5, 185)

Thus, Minimum Value = 0

First Quartile(Q₁) = 0

Median = 0

Third Quartile(Q₃) = 42.5

Maximum Value = 185

Thus, IQR = Q₃ - Q₁ = 42.5

then, Q₁ - 1.5 × IQR = -63.75

and, 1.5 × IQR + Q₃ = 248.75

Since, the minimum value and maximum value is 0 and 185 respectively thus, no value is less than and more than -63.75 and 248.75 respectively.

Hence, no outlier is present in this data.