To solve the problem, we need to find the mean, mode, and median of the runs scored by the 11 players. Let's go through the steps one by one.
### Step 1: Calculate the Mean
The mean is calculated by dividing the total runs scored by the number of players.
1. **Add the runs scored by all players:**
\[
6 + 15 + 120 + 50 + 100 + 80 + 10 + 15 + 8 + 10 + 15
\]
- First, let's add them step by step:
- \(6 + 15 = 21\)
- \(21 + 120 = 141\)
- \(141 + 50 = 191\)
- \(191 + 100 = 291\)
- \(291 + 80 = 371\)
- \(371 + 10 = 381\)
- \(381 + 15 = 396\)
- \(396 + 8 = 404\)
- \(404 + 10 = 414\)
- \(414 + 15 = 429\)
So, the total runs scored is **429**.
2. **Divide by the number of players (11):**
\[
\text{Mean} = \frac{429}{11} = 39
\]
### Step 2: Calculate the Mode
The mode is the number that appears most frequently in the data set.
1. **List the runs scored:**
\[
6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
\]
2. **Count the frequency of each score:**
- 6 appears **1** time
- 15 appears **3** times
- 120 appears **1** time
- 50 appears **1** time
- 100 appears **1** time
- 80 appears **1** time
- 10 appears **2** times
- 8 appears **1** time
The number that appears most frequently is **15** (which appears 3 times).
### Step 3: Calculate the Median
The median is the middle value when the data is arranged in ascending order.
1. **Arrange the data in ascending order:**
\[
6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120
\]
2. **Find the number of observations (n):**
- Here, \(n = 11\) (which is odd).
3. **Calculate the position of the median:**
\[
\text{Median position} = \frac{n + 1}{2} = \frac{11 + 1}{2} = 6
\]
- The 6th value in the ordered list is **15**.
### Summary of Results
- **Mean:** 39
- **Mode:** 15
- **Median:** 15
### Conclusion
The mean, mode, and median are:
- Mean = 39
- Mode = 15
- Median = 15
**Are they the same?** No, the mean (39) is different from the mode and median (both 15).
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