Question

1. which 5 numbers are used to make a boxplot?

a. min, q1, mean, q3, max
b. min, mean, median, mode, max
c. min, iqr, median, range, max
d. min, q1, med, q3, max

1. two students take different exams. jordan scored 85 on a math test (mean = 80, sd = 4). alexis scored 88 on a science test (mean = 82, sd = 6). who performed better relative to their peers?

a. jordan, because her z - score is higher
b. alexis, because her score is further above the mean for her test
c. jordan, because the standard deviation of her test is smaller
d. alexis, because her score is higher

1. if you run the stat/calc/1 command and the output shows the mean is much lower than the median, what does this indicate?

a. the mean is the best measure of center for this dataset
b. the dataset is symmetric
c. the dataset is skewed to the left
d. the median got dragged to the right by some high outliers in the dataset

1. which measure of variation indicates the extent to which the numbers in a dataset vary from the mean of the dataset?

a. standard deviation
b. iqr
c. range
d. median

1. if the lower and upper outlier boundaries for the dataset below are as follows, which statement is true?

lower outlier boundary = 12.75
upper outlier boundary = 26.75
a. there is at least one high outlier but no low outliers
b. there is at least one low outlier but no high outliers
c. there are no outliers in the dataset
d. there are low and high outliers in the dataset

Explanation:

Step1: Boxplot Basics (Question 1)

A boxplot uses the five - number summary: minimum (min), first quartile (Q1), median (med), third quartile (Q3), and maximum (max). Options a, b, c have incorrect components (e.g., mean, mode, IQR in wrong context).

Step2: Z - score Calculation (Question 2)

The z - score formula is \(z=\frac{x - \mu}{\sigma}\). For Jordan: \(z_J=\frac{85 - 80}{4}=1.25\). For Alexis: \(z_A=\frac{88 - 82}{6}=1\). Since \(z_J>z_A\), Jordan has a higher relative performance.

Step3: Mean vs Median (Question 3)

When the mean is much lower than the median, the dataset is skewed to the left. In a left - skewed distribution, there are some small values (outliers or just a long left tail) that pull the mean down, while the median is less affected.

Step4: Measure of Variation (Question 4)

The standard deviation measures the average distance of data points from the mean. IQR measures the spread of the middle 50% of data, range is the difference between max and min, and median is a measure of central tendency.

Step5: Outlier Check (Question 5)

The lower outlier boundary is \(12.75\) and \(minX = 12\). Since \(12<12.75\), but wait, we also check the upper boundary. The upper outlier boundary is \(26.75\) and \(maxX=26\). Since \(12\) is not less than \(12.75\) (by a non - negligible amount considering data precision) and \(26\) is less than \(26.75\), there are no outliers.

Answer:

1. d. min, Q1, med, Q3, max
2. a. Jordan, because her z - score is higher
3. c. The dataset is skewed to the left
4. a. Standard deviation
5. c. There are no outliers in the dataset