The following data gives the number of minutes by which the arrival of 12 trains was delayed at a station: 0 1 0 6 2 50 4 0 1 0 43 25 Find the mean, median, and mode.

Answer

To solve the problem of finding the mean, median, and mode of the given data set, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
The given data is:
0, 1, 0, 6, 2, 50, 4, 0, 1, 0, 43, 25

First, we will arrange the data in ascending order:
0, 0, 0, 0, 1, 1, 2, 4, 6, 25, 43, 50

### Step 2: Calculate the Mean
The mean is calculated by taking the sum of all the observations and dividing it by the number of observations.

1. **Sum of the data**:
\[ 0 + 0 + 0 + 0 + 1 + 1 + 2 + 4 + 6 + 25 + 43 + 50 = 132 \]

2. **Number of observations**: There are 12 observations.

3. **Mean calculation**:
\[ \text{Mean} = \frac{\text{Sum of data}}{\text{Number of observations}} = \frac{132}{12} = 11 \]

### Step 3: Calculate the Median
The median is the middle value of the data when arranged in order. Since we have an even number of observations (12), the median will be the average of the 6th and 7th values in the ordered list.

1. **Identify the middle two terms**:
The 6th and 7th terms in the ordered list are 1 and 2.

2. **Median calculation**:
\[ \text{Median} = \frac{1 + 2}{2} = \frac{3}{2} = 1.5 \]

### Step 4: Calculate the Mode
The mode is the value that appears most frequently in the data set.

1. **Count the frequency of each number**:
- 0 appears 4 times
- 1 appears 2 times
- 2 appears 1 time
- 4 appears 1 time
- 6 appears 1 time
- 25 appears 1 time
- 43 appears 1 time
- 50 appears 1 time

2. **Identify the mode**: The number that appears most frequently is 0.

### Final Results
- **Mean**: 11
- **Median**: 1.5
- **Mode**: 0