The number of challans that are issued per day by the traffic police for traffic violations committed by people at a certain road over two weeks is as follows:
First week: `0, 5, 10, 6, 3, 4, 7`
Second week: `2, 6, 5, 3, 7, 5, 0`
Find mean, median, and mode of the number of challans issued per day for each week.

Answer

To solve the problem, we will calculate the mean, median, and mode for the number of challans issued per day for both weeks separately.

### Step 1: Organizing the Data
**First Week Data:**
0, 5, 10, 6, 3, 4, 7
**Second Week Data:**
2, 6, 5, 3, 7, 5, 0

**Arrange the data in ascending order:**

- **First Week (Ascending Order):**
0, 3, 4, 5, 6, 7, 10

- **Second Week (Ascending Order):**
0, 2, 3, 5, 5, 6, 7

### Step 2: Calculate Mean
**Mean Formula:**
Mean = (Sum of all observations) / (Number of observations)

#### First Week:
- **Sum of Observations:**
0 + 3 + 4 + 5 + 6 + 7 + 10 = 35
- **Number of Observations:** 7

**Mean for First Week:**
Mean = 35 / 7 = 5

#### Second Week:
- **Sum of Observations:**
0 + 2 + 3 + 5 + 5 + 6 + 7 = 28
- **Number of Observations:** 7

**Mean for Second Week:**
Mean = 28 / 7 = 4

### Step 3: Calculate Mode
**Mode Definition:**
Mode is the number that appears most frequently in the data set.

#### First Week:
- **Observations:** 0, 3, 4, 5, 6, 7, 10
- **Frequency:** No number repeats.

**Mode for First Week:**
No mode (since all numbers appear only once).

#### Second Week:
- **Observations:** 0, 2, 3, 5, 5, 6, 7
- **Frequency:** The number 5 appears twice.

**Mode for Second Week:**
Mode = 5

### Step 4: Calculate Median
**Median Definition:**
The median is the middle value when the data is arranged in ascending order. If the number of observations is odd, the median is the middle number.

#### First Week:
- **Observations:** 0, 3, 4, 5, 6, 7, 10
- **Number of Observations:** 7 (odd)
- **Median Position:** (7 + 1) / 2 = 4th term

**Median for First Week:**
4th term = 5

#### Second Week:
- **Observations:** 0, 2, 3, 5, 5, 6, 7
- **Number of Observations:** 7 (odd)
- **Median Position:** (7 + 1) / 2 = 4th term

**Median for Second Week:**
4th term = 5

### Final Results
- **First Week:**
- Mean = 5
- Mode = No mode
- Median = 5

- **Second Week:**
- Mean = 4
- Mode = 5
- Median = 5