Question

2. (20 pts) A certain reaction was run several times using each of two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product. Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst Bare as follows: Catalyst A 3.4 2.6 3.8 4.9 4.1 3.6 4.3 4.4 4.6 2.6 2.9 3.9 3.1 5.2 6.7 2.6 4.8 4.7 4.1 4.0 4.5 Catalyst B 3.4 6.4 3.7 3.5 6.3 1.1 5.0 3.8 59 2.6 5.8 3.1 6.7 4.3 2.5 1.6 5.2 3.8 a) Construct a histogram for the yields of each catalyst. b) Construct comparative boxplots for the yields of the two catalysts. C) Using the boxplots, what differences can be seen between the results of the yields of the two catalysts?

Answer 1

The given data is as follows:

Catalyst A	Catalyst B
4.4	3.4
4.9	6.4
4.1	3.7
3.6	3.5
4.3	6.3
4.4	1.1
3.4	5
4.6	3.8
2.6	5.9
2.9	2.6
3.9	2.9
3.1	5.8
2.6	3.1
5.2	6.7
6.7	4.3
2.6	5.5
4.8	2.5
5.7	1.6
3.8	5.2
4.7	3.8
4.1
4
4.5
4.5

Ans (a):

Histogram:

For Catalyst A:

Make the frequency distribution of the above data as:

Catalyst A	frequency
2.25-2.75	3
2.75-3.25	2
3.25-3.75	2
3.75-4.25	5
4.25-4.75	7
4.75-5.25	3
5.25-5.75	1
5.75-6.25	0
6.25-6.75	1

Then follow the given steps:

1. In your spreadsheet, select the data to use for your histogram graph.
2. Click Insert > Insert Column Chart, and then pick the clustered column graph.
3. Click the graph and then click the icons next to the chart to add finishing touches.

Then the histogram:

Histogram of Catalyst A Frequency ܂ ܐ ܐ oto Catalyst A

For Catalyst B:

Make the frequency distribution of the above data as:

Catalyst B	Frequency
0.5-1.5	1
1.5-2.5	1
2.5-3.5	5
3.5-4.5	5
4.5-5.5	2
5.5-6.5	5
6.5-7.5	1

Then follow the given steps:

1. In your spreadsheet, select the data to use for your histogram graph.
2. Click Insert > Insert Column Chart, and then pick the clustered column graph.
3. Click the graph and then click the icons next to the chart to add finishing touches.

Then the histogram:

Histogram of Catalyst B 55 Frequency Fm Catalyst B

Ans (b):

Boxplots:

Boxplot of Catalyst A, Catalyst B * 6.7 Data Catalyst A Catalyst B

Ans (c):

Box plot is another way to describe a distribution of data. The vertical line within the box represents the median. The box plot is can be used to identify outliers. They can also be used to determine the skewness of a distribution. If the median is located lower side of the box, the distribution is right skewed, and if median is located on the upper side of the box, then the distribution is left skewed. If the median is located in the middle of the box, then the distribution is symmetrical.

Here for catalyst A, median = 4.2 which located at upper side. So, distribution for catalyst A is left skewed. And for catalyst B, median = 3.8 which located at lower side of the box. So, distribution for catalyst B is right skewed.

Catalyst A has an outlier (6.7).

There is much variation in the yields for catalyst B than the yields for catalyst A.