Question

6. The following stem-and-leaf diagram gives the number of patents held by each of a sample of 36 public and private U.S. universities.

A- I

6. The following stem-and-leaf diagram gives the number of patents held by each of a sample of 36 public and private U.S. universities. 0 223 4799 1 11145566689 2 023479 3 004355 419 a) What is the shape of the distribution? Explain. b) What percentage of universities in the sample hold at least 50 patents? (Show work.) 6 9 7 9 9 3 c) Complete the following table to give a five-number summary for the data. Position Value Min Q1 02 Q3 Max e) Find the IQR, the upper and lower fences, and identify any outliers. TQR Lower Fence Upper Fence Outlier(e) f) Draw a box plot over the following x-axis. 10 20 30 40 50 60 70 80 90 100 X

Answer 1

(a)

The distribution of number of patents is skewed to right. It seems that that there is a high outlier.

(b)

Out of 36, 4 are greater than 50 so the required percentage is

(4/50) * 100% = 8%

Hence, the required percentage is 8%.

(c)

minimum value = 02

First quartile: There are 18 data values in first half of data set. That is first quartile will be average of 9th and 10th data values. So

11+ 11 21

Median: It is average of 18th and 19th data values so

19 20 19.5

Third quartile: There are 18 data values in second half of data set. That is third quartile will be average of 27th and 28th data values. So

2a-31334 34.5

Maximum: 93

e)

IQR = Q3-Q1 = 34.5-11 = 23.5

Lower fence:

LF = Q1 _ 1.51QR = 11-1.5. 23.5 =-24.25

Upper fence:

UF = Q3 + 1.5「OR = 34.5 + 1.5 . 23.5 = 69.75

Outliers: 79, 93

(f)

The box plot is

BoxPlot 0 20 40 80 100 120