Q 47. - The Practice of Statistics for AP

Question

El Niño and the monsoon It appears that El Niño, the periodic warming of the Pacific Ocean west of South America, affects the monsoon rains that are essential for agriculture in India. Here are the monsoon rains (in millimeters) for the $23$ strong El Niño years between $1871$ and $2004:: 26$ 

(a) To make a stem plot of these rainfall amounts, round the data to the nearest 10, so that stems are hundreds of millimeters and leaves are tens of millimeters. Make two stem plots, with and without splitting

the stems. Which plot do you prefer?

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

(c) The average monsoon rainfall for all years from $1871$ to $2004$ is about$850$ millimeters. What effect does El Niño appear to have on monsoon rains?

Step-by-Step Solution

Answer

Part (a) A stem plot with the split is preferred over a stem plot without a split as the former

Part (b) 

• Shape: symmetric
• Center: $7$
• Spread: $6$ to $9$

Part (c) Average of rainfall amount is $767$

Part (a) Step 1: Given information

The monsoon rains (in millimeters) for the $23$ strong El Niño years between $1871$ and $2004::26$

628	669	740	651	710	736	717	698	653	604	781	784
790	811	830	858	858	896	806	790	792	957	872

Part (a) Step 2: Concept

Shape: The peak of the dot plot is at  This means that during that season, the team's most common number of goals scored in games (known as the mode) was  The United States women's soccer team scored between one and five goals in the majority of its games. The distribution, however, has a large tail to the right. 

Centre: can be described by selecting a value that divides the observations in half, with the bigger half taking greater values and the smaller half taking lower values. 

The spread of distribution indicates the amount of variability in the data. Giving the smallest and greatest values is one approach to describe the variability.

Part (a) Step 3: Explanation

Round the data to the closest tenth to generate a stem plot of the rainfall amounts.

The amount of rainfall is represented using a stem-plot diagram.

(i) The stem plot without split. 

(ii) The stem plot with a split. 

Therefore, a stem plot with the split is preferred over a stem plot without a split as the former 

Part (b) Step 1: Explanation

The split stem plot's form features a single peak at $7$ The distribution ranges from $6$ to $9$. The distribution has an asymmetrical shape.

Shape: symmetric

Center: $7$

Spread: $6$ to $9$

Part (c) Step 1: Explanation

Between $1871$ and 2004 , the average rainfall amount in El Nino years was: 

sum of the observations/total number of observations=

$$\begin{gathered} \frac{1}{23}\left(628+669+740+........+957+872\right) \\ =\frac{17631}{23} \\ =767 \end{gathered}$$

As result, the Average of rainfall amount is $767$