Question

Grip is applied to produce normal surface forces that compress the object being gripped. Examples indlude two people shaking hands, or a nurse squeezing a patient's forearm to stop bleeding, etc. The data on grip strength (in Newtons (N)) for a sample of 38 individuals is displayed in the box plot provided below. Q1-104, median 150, Q3-230, whickers to: 30 and 329 Grip Strenath 0 100 200 300 400 500 600 700 grip strength (N) Based on this box plot answer the following questions. Explain your reasoning for parts b. and c. a. What is the range of these data? Answer: Answer: Answer: Homework (out of 50): Homework (out of 20): Bonus (out of 4):

Answer 1

Answer

(A) Range of a box plot is equal to the difference between maximum and minimum value

In this case, maximum value =329 and minimum value = 30

So, Range = 329 - 30 = 299

(B) We classify mild outliers in the range of 1.5 times inter-quartile range (IQR), i.e. 1.5IQR below Q1 and 1.5IQR above Q3

similarly, extreme outliers are classified as 3IQR below Q1 and 3IQR above Q3

Inter quarrtile range =IQR = Q3-Q1 = 230-104 = 126

Mild outlier calculation

Q1- 1.5*IQR = 104 - (1.5*126) = -85

Q1+ 1.5*IQR = 104 + (1.5*126) = 293

Extreme outlier calculation

Q1- 3*IQR = 104 - (3*126) = -274

Q1+ 3*IQR = 104 + (3*126) = 482

All the outliers are above the range of mild outliers, so we can say outliers are extreme.

(c) It is already calculated in part (B), i.e. extremen outliers are any value less than 3IQR below Q1 and greater than 3IQR above Q3

Extreme outlier calculation

Q1- 3*IQR = 104 - (3*126) = -274

Q1+ 3*IQR = 104 + (3*126) = 482

So, any value less than -274 and greater than 482 will qualify as an extreme outliers.