https://file.aiquickdraw.com/mathbot/file/1727115156909n1zyn003.jpg

Let's break down the questions and use the frequency diagram provided to answer each part:

### Part (a): **What is the modal class?**
- The modal class is the class interval with the highest frequency. 
- From the diagram, the class interval with the tallest bar is \(125 \leq h < 130\), which has a frequency of 70.
- **Answer: Modal class is \(125 \leq h < 130\).**

### Part (b): **How many stalks are in the class \(120 \leq h < 125\)?**
- From the frequency diagram, the height of the bar corresponding to the class interval \(120 \leq h < 125\) is 64.
- **Answer: There are 64 stalks in the class \(120 \leq h < 125\).**

### Part (c): **How many stalks are at least 120 cm tall?**
- We need to consider all stalks from the class intervals \(120 \leq h < 125\) and \(125 \leq h < 130\).
  - Number of stalks in \(120 \leq h < 125\) = 64.
  - Number of stalks in \(125 \leq h < 130\) = 70.
- Total = \(64 + 70 = 134\).
- **Answer: 134 stalks are at least 120 cm tall.**

### Part (d): **Marcia says, 'This graph shows there are more than double the number of stalks in class \(125 \leq h < 130\) than in \(120 \leq h < 125\).' Explain why she is wrong.**
- Number of stalks in \(125 \leq h < 130\) = 70.
- Number of stalks in \(120 \leq h < 125\) = 64.
- If the number of stalks in \(125 \leq h < 130\) were double that of \(120 \leq h < 125\), it would need to be \(64 \times 2 = 128\).
- However, 70 is not more than double 64. Therefore, Marcia is wrong.
- **Answer: Marcia is wrong because 70 is not more than double 64.**

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Would you like more details on any part of the explanation?

Here are 5 related questions to expand your understanding:
1. How is the mode different from the median or mean in a data set?
2. What would the total number of stalks be, given all the class frequencies?
3. Can you calculate the relative frequency for each class interval?
4. How could you use this frequency diagram to calculate the median height?
5. What other types of graphs could represent this data more effectively?

**Tip:** Always double-check your frequency values and calculations when interpreting histograms to ensure accuracy.

This frequency diagram shows the heights of wheat stalks (main stems). a) What is the modal class? b) How many stalks are in the class 120 ≤ h < 125? c) How many stalks are at least 120 cm tall? d) Marcia says, 'This graph shows there are more than double the number of stalks in class 125 ≤ h < 130 than in 120 ≤ h < 125.' Explain why she is wrong.

Explore how to interpret a frequency diagram displaying the heights of wheat stalks. This problem covers key statistical concepts like modal class and compares frequencies. Suitable for middle school students in Grades 6-8.

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