The problem involves interpreting a cumulative frequency graph to answer two questions:

Questions:

1. (a) Estimate the median height of the oak trees.
2. (b) Estimate the number of oak trees taller than 600 feet.

I’ll break these down step-by-step.

(a) Estimating the Median Height:

The median corresponds to the height at the 50th percentile (middle value) of the cumulative frequency graph. Since there are 200 oak trees:

• The median is at the $\frac{200}{2} = 100$-mark on the cumulative frequency axis.
• Locate 100 on the vertical axis, trace horizontally to the curve, and then trace vertically down to find the corresponding height on the horizontal axis.

From the graph:

• The median height is approximately 400 feet.

(b) Estimating the Number of Trees Taller Than 600 Feet:

To estimate this:

• Find the cumulative frequency at 600 feet (on the horizontal axis).
• Subtract this value from the total number of trees (200).

From the graph:

• The cumulative frequency at 600 feet is approximately 160.
• Trees taller than 600 feet: $200 - 160 = 40$.

Final Answers:

• (a) Median height: 400 feet.
• (b) Trees taller than 600 feet: 40 trees.

Would you like further clarification or visual guidance for these calculations?

5 Related Questions:

1. How can you calculate the interquartile range (IQR) using this graph?
2. What does the slope of the cumulative frequency curve tell us about the distribution of tree heights?
3. How would the median change if there were 300 trees instead of 200?
4. How do we find the 25th and 75th percentiles from this graph?
5. Why is the cumulative frequency graph useful compared to a bar chart?

Tip:

When interpreting cumulative frequency graphs, always identify key percentiles (25th, 50th, 75th) to understand the data distribution better.