Question

The ages of some patients admitted to a certain hospital during a particular week were as follows: 48, 109, 31, 54, 11, 37, 18, 64, 99 , 61, 43, 40, 71, 52, 12, 65, 54, 42, 34, 62, 74, 48, 29, 19, 28, 30, 36, 49, 68, 35, 57, 126, 27, 58, 78, 72, 40, 22, 89, 61, 92, 84,100, 101, 96, 113, 79, 85, 21, 67, 94, 25, 69, 108, and 105. Construct the Stem and Leaf display from the data and list the data in an array. Also give a real-life example on the use of stem and leaf display. b- Following data is about the CGPA of two classes. By using the coefficient of variation determine which class performance is consistence Class A 2.30 2.50 3.12 3.01 2.99 3.21 3.97 3.20 2.67 Class B 1.59 4.00 2.45 3.98 1.90 2.56 3.33 3.89 2.67

Answer 1

a) Stem and Leaf plot

Answer:

Stem	Leaf
1	1	2	8	9	.	.	.	.
2	1	2	5	7	8	9	.	.
3	0	1	4	5	6	7	.	.
4	0	0	2	3	8	8	9
5	2	4	4	7	8	.	.	.
6	1	1	2	4	5	7	8	9
7	1	2	4	8	9	.	.	.
8	4	5	9	.	.	.	.	.
9	2	4	6	9	.	.	.	.
10	0	1	5	8	9	.	.	.
11	3	.	.	.	.	.	.	.
12	6	.	.	.	.	.	.	.

Explanation:

The stemplot is obtained in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: Select the data values then DATA > Sort > Continue with the current selection > OK. then Select Sort by: Treatment, Sort On: Values, Order: Smallest to Largest. The screenshot is shown below,

Step 3: Make a stem by taking the tens' digit from the data values as shown below,

Stem
1
2
3
4
5
6
7
8
9
10
11
12

Step 4: Now, write the unit digit in front of the respective tens' digit. The stemplot is obtained. The screenshot is shown below,

(Key: 1|1 corresponds to 11, 12|6 corresponds to 126)

b) coefficient of variation

Answer:

Class B is more consistent compared to Class A.

Explanation:

The coefficient of variance is obtained using the formula,

where the sample means and the sample standard deviation values are obtained in excel using the function =AVERAGE() and =STDEV(). The screenshot is shown below,

For Class A => coefficient variation = 6.1679

For Class B => coefficient variation = 3.2208

Conclusion:

The coefficient of variation tells the dispersion of the data values around the mean value such that larger the CV, the larger will be the dispersion of the data values.

Now, the performance of the class will be consistent if the CV is smaller. Since the CV is smaller for Class B, we can conclude that Class B is more consistent compared to Class A.