Question

1. eighteen different players on a college lacrosse team scored at least one goal in a recent season. the number of goals scored by each of these players is listed along with the summary statistics. 1,1,2,2,6,8,8,10,12,14,18,19,24,32,50,51,107,121

n	mean	sd	min	q1	med	q3	max
18	27	35.12	1	6	13	32	121

a. use the 1.5×iqr method to identify any outliers. show your work.
b. use the 2×sd method to identify any outliers. show your work.
c. create a boxplot.

1. a large high school has 148 teachers. the box - plot shows the distribution of the number of years of experience.

!box - plot(https://content.bartleby.com/qna-images/question/7c8c8133-9782-4c0d-8644-9c8c919c8d89/089c0c94-8661-4e11-859d-9c8c919c8d89/20230717164949809090.png)a. find and interpret the median number of years teaching experience.
b. what percent of the teachers have 7 or more years of teaching experience?
c. about how many of the teachers have between 7 and 23 years of experience?

Explanation:

Step1: Calculate IQR for 1.5 x IQR method

IQR = $Q_3 - Q_1$. Given $Q_1 = 6$ and $Q_3=32$, so IQR = $32 - 6=26$.
Lower - fence = $Q_1-1.5\times IQR=6 - 1.5\times26=6 - 39=- 33$. Upper - fence = $Q_3 + 1.5\times IQR=32+1.5\times26=32 + 39 = 71$. Values less than - 33 or greater than 71 are outliers. So the outliers are 107, 121.

Step2: Calculate bounds for 2 x SD method

Given mean $\bar{x}=27$ and SD = 35.12. Lower - bound = $\bar{x}-2\times SD=27-2\times35.12=27 - 70.24=-43.24$. Upper - bound = $\bar{x}+2\times SD=27 + 2\times35.12=27+70.24 = 97.24$. Values less than - 43.24 or greater than 97.24 are outliers. So the outliers are 107, 121.

Step3: Create box - plot (description)

The box - plot has a minimum value of 1, $Q_1 = 6$, median (med) = 13, $Q_3 = 32$, and a maximum value of 121. The box extends from $Q_1$ to $Q_3$ with a line at the median. Whiskers extend from the box to the minimum and maximum non - outlier values (in this case, the minimum is 1 and the maximum non - outlier value within the 1.5 x IQR bounds is 51). Outliers (107, 121) are plotted as individual points.

For the high - school teachers problem:

Step4: Find median from box - plot

The median is the value at the line inside the box. From the box - plot, the median number of years of teaching experience is 15 years. This means that half of the 148 teachers have 15 or fewer years of teaching experience and half have 15 or more years of teaching experience.

Step5: Calculate percentage with 7 or more years

The left - hand side of the box starts at approximately 7. Since the box and whisker to the right represent 75% of the data (the box represents the middle 50% and the right - hand whisker represents 25% of the data), 75% of the 148 teachers have 7 or more years of teaching experience.

Step6: Estimate number between 7 and 23 years

The value 23 is approximately at the right - hand side of the box ($Q_3$). The data between 7 and 23 years represents the middle 50% of the data. So the number of teachers with between 7 and 23 years of experience is approximately $0.5\times148 = 74$.

Answer:

a. Outliers using 1.5 x IQR method: 107, 121
b. Outliers using 2 x SD method: 107, 121
c. Box - plot: Minimum = 1, $Q_1 = 6$, Median = 13, $Q_3 = 32$, Maximum non - outlier (within 1.5 x IQR) = 51, Outliers = 107, 121
For high - school teachers:
a. Median number of years of teaching experience is 15 years. Half of the teachers have 15 or fewer years of teaching experience and half have 15 or more years of teaching experience.
b. 75% of the teachers have 7 or more years of teaching experience.
c. Approximately 74 teachers have between 7 and 23 years of experience.