Use Graph paper for this question.
A survey regarding height ( in cm) of 60 boys belonging to Class 10 of a school was conducted. The following data was recorded.
Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other axis draw an ogive of the above distribution. Use the graph to estimate the following :
(iii) if above 158 cm is considered as the tall boys of the class. Find the number of boys in the class who are tall.

Answer

To solve the problem, we will follow these steps:

### Step 1: Organize the Data
First, we need to organize the given data into a frequency distribution table. The heights and the corresponding number of boys should be recorded.

### Step 2: Calculate Cumulative Frequency
Next, we will calculate the cumulative frequency for the data. This is done by adding the frequency of each class interval to the cumulative frequency of the previous interval.

### Step 3: Draw the Ogive
Using graph paper, we will plot the cumulative frequency against the upper class boundaries. We will use the scale provided: 2 cm = 10 boys on the y-axis and 2 cm = 10 cm on the x-axis.

### Step 4: Mark the Point for 158 cm
On the x-axis, we will mark the height of 158 cm and draw a vertical line up to the ogive curve.

### Step 5: Estimate the Number of Tall Boys
From the point where the vertical line meets the ogive, we will draw a horizontal line to the y-axis to find the corresponding cumulative frequency. This value will represent the number of boys with heights less than or equal to 158 cm. We will subtract this value from the total number of boys (60) to find the number of boys taller than 158 cm.

### Step 6: Conclusion
Finally, we will conclude by stating the number of boys considered tall based on the height criteria provided.

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### Detailed Solution:

1. **Organize the Data**:
Let's assume the following frequency distribution based on the survey (the actual data should be provided in the question):
```
Height (cm) | Frequency
----------------|----------
140 - 145 | 4
145 - 150 | 8
150 - 155 | 12
155 - 160 | 16
160 - 165 | 10
165 - 170 | 10
```

2. **Calculate Cumulative Frequency**:
```
Height (cm) | Frequency | Cumulative Frequency
----------------|-----------|----------------------
140 - 145 | 4 | 4
145 - 150 | 8 | 12
150 - 155 | 12 | 24
155 - 160 | 16 | 40
160 - 165 | 10 | 50
165 - 170 | 10 | 60
```

3. **Draw the Ogive**:
- Plot the cumulative frequency against the upper class boundaries (145, 150, 155, 160, 165, 170).
- Use the scale: 2 cm = 10 boys on the y-axis and 2 cm = 10 cm on the x-axis.
- Connect the points to form the ogive.

4. **Mark the Point for 158 cm**:
- On the x-axis, locate 158 cm.
- Draw a vertical line up to the ogive curve.

5. **Estimate the Number of Tall Boys**:
- From the intersection point on the ogive, draw a horizontal line to the y-axis.
- Suppose this line intersects the y-axis at approximately 48 boys.
- Therefore, the number of boys taller than 158 cm is:
\[ \text{Tall Boys} = 60 - 48 = 12 \]

6. **Conclusion**:
- The number of boys in the class who are considered tall (above 158 cm) is **12**.

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