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The question in the image asks to calculate the "mean deviation about the median" using a frequency distribution of students' heights.

The data presented is:

| Height Range (cm) | No. of Students |
|------------------|-----------------|
| 95 - 105         | 9               |
| 105 - 115        | 13              |
| 115 - 125        | 25              |
| 125 - 135        | 30              |
| 135 - 145        | 13              |
| 145 - 155        | 10              |

### Steps to solve:

1. **Find the median** of the dataThe question in the image asks to calculate the "mean deviation about the median" using a frequency distribution of students' heights.

The data presented is:

| Height Range (cm) | No. of Students |
|------------------|-----------------|
| 95 - 105         | 9               |
| 105 - 115        | 13              |
| 115 - 125        | 25              |
| 125 - 135        | 30              |
| 135 - 145        | 13              |
| 145 - 155        | 10              |

### Steps to solve:

1. **Find the median** of the 
   - First, calculate the cumulative frequency.
   - The median class is identified by locating the class where the cumulative frequency surpasses \( N/2 \), where \( N \) is the total number of students.

2. **Calculate the mean deviation about the median**:
   - Use the median as a reference point to compute the deviation of each class.
   - Find the absolute deviations of the class midpoints from the median.
   - Compute the weighted sum of these deviations, divided by the total number of students.

Let me compute this.The median of the data is \( 126.0 \) cm. The mean deviation about the median is approximately \( 11.34 \) cm.

Would you like a detailed breakdown of the steps or have any questions? Here are some related questions for further exploration:

1. How would the process change if we were calculating the mean deviation about the mean instead?
2. Can you explain the significance of the median in a frequency distribution?
3. What is the purpose of calculating the mean deviation in statistics?
4. How would this calculation differ if there were unequal class intervals?
5. What are other measures of dispersion, and how do they compare to mean deviation?

**Tip:** Mean deviation provides an idea of the average distance between data points and a central value, giving insight into the variability of the data.

Calculate the mean deviation about the median for the given frequency distribution of students' heights.

Learn how to calculate the mean deviation about the median using a frequency distribution of students' heights ranging from 95 cm to 155 cm. This problem demonstrates key statistical concepts such as cumulative frequency and the importance of the median. Suitable for Grades 10-12.

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