show me how to do (iv) How many apples from those picked weighed less than 42 g?

To determine how many apples weighed less than 42 grams using a box-and-whisker plot, you can follow these steps:

### Step 1: Identify the position of 42 grams on the box-and-whisker plot
- Look at the box-and-whisker plot and locate the 42-gram mark on the horizontal axis. This will show you where 42 grams falls relative to the other data points.

### Step 2: Determine the quartile where 42 grams falls
- The box-and-whisker plot is divided into quartiles:
  - **Q1 (First Quartile):** The value below which 25% of the data lies.
  - **Q2 (Median):** The value below which 50% of the data lies.
  - **Q3 (Third Quartile):** The value below which 75% of the data lies.
  
  If 42 grams falls to the left of Q1, then it is in the first quartile. If it falls between Q1 and the median, it is in the second quartile, and so on.

### Step 3: Estimate the number of apples
- Since there are 300 apples in total:
  - Each quartile represents 25% of the apples. 
  - 25% of 300 apples = 75 apples per quartile.
  
  Depending on where 42 grams falls:
  - If 42 grams is in the first quartile (left of Q1), then fewer than 75 apples weigh less than 42 grams.
  - If 42 grams is in the second quartile (between Q1 and the median), then fewer than 150 apples (75 from Q1 + some from Q2) weigh less than 42 grams.

### Step 4: Refine the estimate (if possible)
- If the 42 grams mark is exactly at the first quartile (Q1), then exactly 75 apples weigh less than 42 grams. If it’s somewhere within the quartile, you would estimate a proportion based on where it lies within that section.

### Example:
Let's assume:
- **Q1 (First Quartile)** is at 40 grams.
- **Median (Q2)** is at 50 grams.

If 42 grams is just above Q1 but before the median:
- You know 75 apples weigh less than 40 grams (Q1).
- Since 42 grams is between Q1 and the median, there are more than 75 but fewer than 150 apples under 42 grams.

Without exact positions, it’s an estimate, but you can say the number of apples under 42 grams is slightly more than 75.

### Conclusion:
To get the precise number of apples under 42 grams, you need to know exactly where 42 grams falls in the plot and the distribution within that quartile.

Would you like more details on how to make these estimates more accurate?

### Further Questions:
1. How can the exact position of 42 grams be determined from the plot?
2. What if the plot shows outliers below 42 grams?
3. How does changing the number of apples affect quartile distribution?
4. How would you calculate the exact number of apples if 42 grams was the median?
5. Can the box-and-whisker plot help in identifying skewness in apple weights?

**Tip:** Understanding quartiles and how they divide your data is crucial when interpreting box-and-whisker plots. Each quartile represents an equal number of data points, which helps in estimating quantities like in this problem.

Learn how to use box-and-whisker plots to find out how many apples weighed less than 42 grams. This detailed guide includes step-by-step instructions on interpreting quartiles and estimating quantities from the plot. Suitable for advanced high school students.

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