The histogram below represents the scores obtained by 25 students in a Mathematics mental test. Use the data to,
(i) Frame a frequency distribution table
(ii) To calculate mean

Answer

To solve the problem step by step, we will first create a frequency distribution table based on the histogram data provided, and then we will calculate the mean of the scores.

### Step 1: Frame a Frequency Distribution Table

1. **Identify the Class Intervals**: From the histogram, we can identify the class intervals as follows:
- 0 to 10
- 10 to 20
- 20 to 30
- 30 to 40
- 40 to 50

2. **Count the Frequencies**: We will count the number of students (frequency) for each class interval:
- For 0 to 10: 2 students
- For 10 to 20: 5 students
- For 20 to 30: 8 students
- For 30 to 40: 4 students
- For 40 to 50: 6 students

3. **Create the Table**:
| Class Interval | Frequency (f) |
|----------------|----------------|
| 0 - 10 | 2 |
| 10 - 20 | 5 |
| 20 - 30 | 8 |
| 30 - 40 | 4 |
| 40 - 50 | 6 |
| **Total** | **25** |

### Step 2: Calculate the Mean

1. **Find the Midpoint (x) for Each Class Interval**:
- For 0 to 10: Midpoint = (0 + 10)/2 = 5
- For 10 to 20: Midpoint = (10 + 20)/2 = 15
- For 20 to 30: Midpoint = (20 + 30)/2 = 25
- For 30 to 40: Midpoint = (30 + 40)/2 = 35
- For 40 to 50: Midpoint = (40 + 50)/2 = 45

2. **Calculate the Product of Midpoint and Frequency (fx)**:
- For 0 to 10: fx = 5 * 2 = 10
- For 10 to 20: fx = 15 * 5 = 75
- For 20 to 30: fx = 25 * 8 = 200
- For 30 to 40: fx = 35 * 4 = 140
- For 40 to 50: fx = 45 * 6 = 270

3. **Create a New Table with fx**:
| Class Interval | Frequency (f) | Midpoint (x) | fx |
|----------------|----------------|---------------|------|
| 0 - 10 | 2 | 5 | 10 |
| 10 - 20 | 5 | 15 | 75 |
| 20 - 30 | 8 | 25 | 200 |
| 30 - 40 | 4 | 35 | 140 |
| 40 - 50 | 6 | 45 | 270 |
| **Total** | **25** | | **695** |

4. **Calculate the Mean**:
- Use the formula for mean:
\[ \text{Mean} = \frac{\sum (fx)}{\sum (f)} = \frac{695}{25} = 27.8 \]

### Final Result
The mean of the scores obtained by the students is **27.8**.

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