MATH SOLVE

4 months ago

Q:
# (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.

Accepted Solution

A:

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 × IQRand 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 = 0First Quartile(Q₁) = 7.5Median = 80Third Quartile(Q₃) = 122.5Maximum Value = 440Thus, IQR = Q₃ - Q₁ = 115then, Q₁ - 1.5 × IQR = -165and, 1.5 × IQR + Q₃ = 295Since, 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 = 0First Quartile(Q₁) = 0Median = 0Third Quartile(Q₃) = 42.5Maximum Value = 185Thus, IQR = Q₃ - Q₁ = 42.5then, Q₁ - 1.5 × IQR = -63.75and, 1.5 × IQR + Q₃ = 248.75Since, 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.