The runs scored in a cricket match by 11 players are as follows :
6, 15, 120, 50, 100, 80, 10, 15, 18, 10, 15
Find the mean, mode and median of this data. Are the three same ?

Answer

To solve the problem, we need to find the mean, median, and mode of the given runs scored by 11 players: 6, 15, 120, 50, 100, 80, 10, 15, 18, 10, 15.

### Step 1: Calculate the Mean
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]

First, we need to find the sum of all the runs:
\[ 6 + 15 + 120 + 50 + 100 + 80 + 10 + 15 + 18 + 10 + 15 = 439 \]

Now, we divide the sum by the total number of observations (which is 11):
\[ \text{Mean} = \frac{439}{11} \approx 39.91 \]

### Step 2: Calculate the Median
To find the median, we first need to arrange the data in ascending order:
\[ 6, 10, 10, 15, 15, 15, 18, 50, 80, 100, 120 \]

Since there are 11 observations (an odd number), the median is the middle value. We can find the position of the median using the formula:
\[ \text{Median position} = \frac{n + 1}{2} \]
where \( n \) is the total number of observations.

Calculating:
\[ \text{Median position} = \frac{11 + 1}{2} = 6 \]

The 6th term in the ordered list is 15. Thus, the median is:
\[ \text{Median} = 15 \]

### Step 3: Calculate the Mode
The mode is the value that appears most frequently in the data set. Looking at our ordered data:
\[ 6, 10, 10, 15, 15, 15, 18, 50, 80, 100, 120 \]
The number 15 appears 3 times, which is more than any other number.

Thus, the mode is:
\[ \text{Mode} = 15 \]

### Summary of Results
- Mean: \( \approx 39.91 \)
- Median: \( 15 \)
- Mode: \( 15 \)

### Final Comparison
Now we compare the three values:
- Mean: \( \approx 39.91 \)
- Median: \( 15 \)
- Mode: \( 15 \)

**Conclusion**: The mean, median, and mode are not the same. The mean is approximately 39.91, while the median and mode are both 15.

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