(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.

(i) Outlier is present

(ii) Outlier is not present.

Step-by-step 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.