The enrollment of several small colleges are listed below. Construct a stem and

Question

The enrollment of several small colleges are listed below. Construct a stem and leaf plot of the enrollments. then answer each following question.

College

Enrollment

Miller Business School

1342

Capital College

1685

Para Professional Institute

1013

Parke College

2350

State Community

3781

Fashion Institute

1096

College of Arts and design

1960

Franklin Community College

3243

(a) Using the 5-summmary strategy, what are your lowest, Q1, Q2, Q3, Highest data? What is your IQR?

(b) What is the mode?

College

Enrollment

Miller Business School

1342

Capital College

1685

Para Professional Institute

1013

Parke College

2350

State Community

3781

Fashion Institute

1096

College of Arts and design

1960

Franklin Community College

3243

Explanation / Answer

Put the data into order then round and truncate into two digits

Back to back stem and leaf plot

Rounded Truncated

7 3 1 0 1 0 0 3 6 9

4 0 2 3

8 2 3 2 7

a) Five number summary:

Here, we took the truncated data.

  Step 1: Put your numbers in ascending order (from smallest to largest). For this particular data set, the order

is:

10 , 10 , 13 , 16 , 19 , 23 , 32 , 37

Step 2: Find the minimum and maximum for your data set.

the minimum (the smallest number) is 10 and the maximum (the largest number) is 37

Step 3: Find the median. The median is the middle number

(16 + 19) /2 = 17.5

Step 4: Place parentheses around the numbers above and below the median.

   ( 10 , 10 , 13, 16) (19 , 23 , 32 , 37)

Find Q1 and Q3. Q1 can be thought of as a median in the lower half of the data, and Q3 can be thought of as a median for the upper half of data

Q1 = (10+13) / 2 = 11.5 , Q3 = (23 + 32) / 2 = 27.5

IQR = Q3 - Q1 = 27.5 - 11.5 = 16

Lowest = 10 , Q1 = 11.5 , Q2 = 17.5 , Q3 = 27.5 , Highest = 37

b) A number that appears most often is the mode.

Mode is 10

Enrollment Normal Rounded(2 digits) Truncated(2 digits) 1013 10 10 1096 11 10 1342 13 13 1685 17 16 1960 20 19 2350 24 23 3243 32 32 3781 38 37

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