Question No: 2

From the following table provides data on marks obtained by 50 students in a class for the 

subject of statistics

Marks 10-20 20-30 30-40 40-50 50-60 60-70

Frequency 2 8 7 10 8 6

Draw a histogram and write your observations.

To draw a histogram for the given data, we need to follow these steps:

1. **Marks Range**: We have marks in the intervals of 10-20, 20-30, 30-40, 40-50, 50-60, and 60-70.
2. **Frequency**: The number of students in each interval is given as 2, 8, 7, 10, 8, and 6, respectively.

### Drawing the Histogram

1. **Horizontal Axis (X-axis)**: This will represent the marks intervals.
2. **Vertical Axis (Y-axis)**: This will represent the frequency of students.

Here's the histogram:

```
Frequency
  ^
10|
 9|
 8|                       _____     _____
 7|              _____   |     |   |     |
 6|             |     |  |     |   |     |
 5|             |     |  |     |   |     |
 4|             |     |  |     |   |     |
 3|             |     |  |     |   |     |
 2|   _____     |     |  |     |   |     |
 1|  |     |    |     |  |     |   |     |
 0|__|_____|____|_____|__|_____|___|_____|
   10-20  20-30 30-40  40-50  50-60  60-70
```

### Plotting the Histogram

To accurately plot the histogram, we'll use Python to visualize it.

```python
import matplotlib.pyplot as plt

# Data
marks = ['10-20', '20-30', '30-40', '40-50', '50-60', '60-70']
frequency = [2, 8, 7, 10, 8, 6]

# Create the histogram
plt.bar(marks, frequency, color='blue', edgecolor='black')

# Titles and labels
plt.title('Histogram of Marks Obtained by Students')
plt.xlabel('Marks Range')
plt.ylabel('Frequency')

# Display the histogram
plt.show()
```

### Observations

1. **Most Frequent Marks Range**: The range with the highest frequency of students is 40-50, with 10 students scoring within this range.
2. **Least Frequent Marks Range**: The range with the lowest frequency of students is 10-20, with only 2 students scoring within this range.
3. **Symmetry**: The distribution of marks is relatively symmetrical, with a peak at the 40-50 range and a decline on either side.
4. **Performance Distribution**: The marks are fairly distributed across the ranges, with no single range dominating entirely. This indicates a varied performance among students.
5. **Central Tendency**: The central tendency appears around the 40-50 range, suggesting that most students score around this range.

Would you like any more details or have any questions?

### Suggested Questions

1. How can I calculate the mean marks from this data?
2. What is the median mark range of this distribution?
3. How do I determine the mode of this data set?
4. Can you explain the concept of skewness in this histogram?
5. How can I compare this histogram with another subject's marks?

### Tip

When analyzing histograms, always check for the shape of the distribution (e.g., normal, skewed, bimodal) to understand the overall trend and performance better.

Learn how to draw a histogram for statistics class data with step-by-step instructions. This problem involves analyzing marks obtained by students in different ranges and visualizing the distribution using a histogram. Suitable for high school students studying statistics.

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