Here are the monsoon rains (in millimeters) for the 23 strong El Nino years between 1871 and 2004:


628 669 740 651 710 717 698 653 604 781 784 790 811 830 858 896

806 790 792 957 872

a. To make the stemplot of these rainfall amounts, round the data to the nearest 10, so that are hundress of millimeters and leaves are tens of millimeters. Make 2 stemplots, with and without splitting the stems. Which plot so you prefer?

b. Describe the shape, center, and spread of the distribution.

c. The average monsoon rainfall for all years form 1871 to 2004 is about 850 millimeters. What effect does El Nino appear to have on monsoon rains?

A. The stemplot with splitting the stems would be preferable, as it provides more detail about the data. The stemplot would look like this:

Stem | Leaves
6 | 0, 8, 8
7 | 0, 0, 4, 6, 8, 8, 8, 8, 9
8 | 0, 0, 1, 1, 2, 5, 6, 8, 8, 9
9 | 5, 7

B. The shape of the distribution is slightly skewed to the left, with a center around 800 millimeters and a spread between 600 and 950 millimeters.

C. El Nino appears to have a negative effect on monsoon rains, as the average monsoon rainfall for El Nino years is lower than the average monsoon rainfall for all years.

a. To create a stemplot of the rainfall amounts, you will need to round the data to the nearest 10. This means that the hundreds of millimeters will be represented by the stems, and the tens of millimeters will be represented by the leaves.

Stemplot without splitting the stems:
6 | 28 51 04
7 | 10 17 53 04 64 90 92 72 72
8 | 11 20 06 08 30 57 06

Stemplot with splitting the stems:
6 | 2 8
6 | 5 9
7 | 0 1 0 1 1 7 7 8 7 7 7 1 3 0 8
8 | 0 6 3 0 5 7 0 2 9 2
9 | 5 7 2

In the stemplot without splitting the stems, the stems are not split into two rows when there are more than 9 leaves. However, in the stemplot with splitting the stems, the stems are split into two rows for better readability.

The preferred plot would depend on the purpose and preference of the viewer. If you want a more detailed visualization and can handle the additional rows, then the stemplot with splitting the stems would be better. If you prefer a simpler representation, then the stemplot without splitting the stems may be preferred.

b. To describe the shape, center, and spread of the distribution, we can use the stemplot to make observations:

Shape: The shape of the distribution is unimodal, with a concentration of values around the stem 8. It appears to be slightly skewed to the right, as there are fewer values on the left side of the distribution.

Center: The center of the distribution can be estimated as the median. In this case, it falls around the stem 8, indicating that the median rainfall amount is around 80-89 millimeters.

Spread: The spread of the distribution can be estimated by looking at the range of values. In this case, the lowest rainfall recorded is 28 millimeters, while the highest is 957 millimeters. Therefore, the range is approximately 929 millimeters, indicating a relatively large spread in the data.

c. Based on the given data, it appears that El Nino has a varying effect on monsoon rains. Some El Nino years have relatively lower rainfall amounts, such as 604 millimeters, while others have higher amounts, such as 957 millimeters. The average monsoon rainfall for all years is around 850 millimeters, and it can be observed that there is substantial variation around this average in the El Nino years. Therefore, El Nino seems to have an impact on monsoon rains, but the specific effect can vary widely.

a. To create a stemplot with the rounded rainfall data, we'll need to split the stems into tens digit and ones digit.

With split stems:
60 | 4
65 | 3
68 | 99
70 | 166789
80 | 0256778
90 | 57

Without split stems:
6 | 46588899
7 | 01017
8 | 06677899
9 | 57

I prefer the plot without splitting the stems as it gives a clearer visualization of the distribution.

b. The shape of the distribution appears to be right-skewed. The center of the distribution can be estimated as around the mid-800s, and the spread of the distribution ranges from around 600 to 900 millimeters.

c. El Nino appears to have a varying effect on monsoon rains. Some El Nino years have lower rainfall amounts than average, while others have higher amounts. However, without further analysis, it is difficult to determine the exact impact of El Nino on monsoon rains.