Let's work through the questions in the image one by one.

For question 19, we are analyzing the corrected long-jump distance data.

Part (a) asks:

What shape would the distribution of corrected long-jump distance have?

• We can infer the shape of the distribution from the dot plot. The plot seems to have a slight right skew, meaning that most of the data points are concentrated towards the left (lower values), with fewer points trailing off to the right (higher values).

Thus, the shape of the distribution is slightly skewed to the right.

Part (b) asks:

Find the median of the distribution of corrected long-jump distance.

• The median of the long-jump distance is provided as 574.5 cm in the numerical summary below the dot plot.

So, the median of the corrected long-jump distance is 574.5 cm.

Part (c) asks:

Calculate the interquartile range (IQR) of the distribution of corrected long-jump distance.

• The IQR is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

  • Q3 = 581.5 cm
  • Q1 = 567.5 cm

  So, the IQR = Q3 - Q1 = 581.5 - 567.5 = 14 cm.

Let me know if you'd like further explanations or additional details on any of these answers!

Related questions:

1. How does the skewness of a distribution affect its mean and median?
2. What is the significance of the interquartile range in describing the spread of a dataset?
3. How does outlier data affect the shape of a distribution in general?
4. Why is the IQR more robust to outliers compared to the range?
5. What are the possible sources of error in recording jump distances, and how might they affect the distribution?

Tip:

To quickly assess the shape of a distribution, observe whether the bulk of the data points are more spread out on one side. A right skew has more data on the left and a tail on the right, while a left skew is the opposite.