Question

1. what is the iqr? (lesson 1 - 11)

a. 5 branches
b. 7 branches
c. 10 branches
d. 12 branches

1. select all the distribution shapes for which the mean and median must be approximately the same. (lesson 1 - 10)

a. bell - shaped
b. bimodal
c. skewed
d. symmetric
e. uniform

Explanation:

Step1: Recall IQR definition

IQR (Inter - Quartile Range) is $Q_3 - Q_1$, where $Q_3$ is the third - quartile and $Q_1$ is the first - quartile. In a box - and - whisker plot, the left edge of the box is $Q_1$ and the right edge of the box is $Q_3$. From the box - and - whisker plot, $Q_1 = 8$ and $Q_3=13$.

Step2: Calculate IQR

$IQR=Q_3 - Q_1=13 - 8 = 5$

Step3: Recall mean - median relationship

For symmetric distributions (including bell - shaped and uniform distributions), the mean and median are approximately the same. Bell - shaped is a type of symmetric distribution, and in a uniform distribution, the data is evenly spread, so mean = median. A bimodal distribution may not have mean = median, and a skewed distribution has a pulled - out tail which affects the mean more than the median.

Answer:

1. A. 5 branches
2. A. bell - shaped, D. symmetric, E. uniform