Question

analyzing the shape of data code 1
mild

1. which of the following box - plots is skewed to the left? put a star to the right of that graph.
2. which of the box plots has greater variability? explain your reasoning.

medium

1. the histogram shown at the right displays the number of toys juniors in the national honor society donated to charity.

is this data skewed or symmetric? explain.

1. for which histogram below is it true that the mean is greater than the median? circle one.

graph a
graph b
graph c

Explanation:

Step1: Recall left - skewed box - plot characteristics

In a left - skewed box - plot, the whisker on the left side is longer and the median is closer to the third quartile. We would need to visually inspect the given box - plots to identify the left - skewed one.

Step2: Recall variability in box - plots

Variability in a box - plot can be measured by the length of the box (IQR: $Q_3 - Q_1$) and the length of the whiskers. A box - plot with a larger IQR and longer whiskers has greater variability. Compare the IQRs and whisker lengths of the given box - plots.

Step3: Recall skewness and symmetry in histograms

A symmetric histogram has a similar shape on both sides of the center. If the tail of the histogram extends more to the left, it is left - skewed; if it extends more to the right, it is right - skewed. Inspect the given histogram of toys donated.

Step4: Recall relationship between mean and median in skewed histograms

In a right - skewed histogram, the mean is greater than the median because the long right - tail pulls the mean in the direction of the tail. Inspect Graph A, Graph B and Graph C to find the right - skewed one.

Answer:

1. (No box - plots shown in the text for specific answer, but should visually identify left - skewed box - plot)
2. (No box - plots shown in the text for specific answer, but should compare IQRs and whisker lengths and explain)
3. The given histogram is skewed. The left side has a higher frequency and the right - hand side has a long tail, indicating right - skewness.
4. Graph C is right - skewed, so the mean is greater than the median.