Question

monica analyzes the number of inches of rain that fell on her desert ranch. here is the data for the last several years. each circle shows the number of inches of rain in one year. the mean number of inches is 1.4 and the median number of inches is 1.3. there was a large increase in the rainfall, with 9.8 inches in the last year. question 1: which of the lines (a, b, c, or d) shown above is most likely to be the mean after including the increased rainfall? a b c d question 2: which of the lines (a, b, c, or d) is most likely to be the median after including the increased rainfall? a b c d question 3: which of the following descriptive statistics are strongly affected by outliers? choose all that apply. mode average median range question 4: in which of the cases should monica throw out or change the outlier? choose all that apply. the rain gauge that measured the rainfall has a broken spring while the rain on her ranch increased, across the state, there was a large decrease in rainfall almost all of the additional rain fell in only one big storm monica entered the data and hit a wrong number on the keyboard

Explanation:

Step1: Count original data points

From the first dot plot, count the circles: 4 circles at ~1 inch, 1 at ~1.5 inches, 1 at ~2 inches. Total $n=6$.

Step2: Calculate original total rainfall

Use mean formula $\text{Total} = \text{Mean} \times n$
$\text{Original Total} = 1.4 \times 6 = 8.4$

Step3: Calculate new total and mean

Add 9.8 inches, new $n=7$.
$\text{New Total} = 8.4 + 9.8 = 18.2$
$\text{New Mean} = \frac{18.2}{7} = 2.6$

Step4: Find new median

Original data sorted: $[x_1,x_2,x_3,x_4,x_5,x_6]$ (median is average of $x_3,x_4=1.3$). Add 9.8, sorted data has 7 points, median is 4th value, same as original $x_4=1.3$.

Step5: Identify outlier-sensitive stats

Recall properties: mean (average) and range are pulled by outliers; median/mode are not.

Step6: Validate outlier removal cases

Only remove outliers if data is erroneous (broken gauge, data entry error).

Answer:

Question 1: B
Question 2: A
Question 3: Average, Range
Question 4: The rain gauge that measured the rainfall has a broken spring; Monica entered the data and hit a wrong number on the keyboard