The runs scored in a cricket match by 11 players is as follows:6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15Find the mean, mode and median of this data. Are the three same?

Options

A. `" mean = 39, median = 15, mode = 15"`
B. `" mean = 40, median = 16, mode = 16"`
C. `" mean = 38, median = 11, mode = 11"`
D. `" mean = 33, median = 12, mode = 12"`

Explanation

To find the mean, mode, and median of the runs scored by the 11 players, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
First, we need to arrange the runs scored by the players in ascending order.

**Data:** 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

**Arranged Data:** 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120

### Step 2: Calculate the Mean
The mean is calculated by dividing the total sum of the data by the number of observations.

1. **Sum of the Runs:**
- \(6 + 8 + 10 + 10 + 15 + 15 + 15 + 50 + 80 + 100 + 120 = 429\)

2. **Number of Players (n):** 11

3. **Mean Calculation:**
- Mean = Total Runs / Number of Players
- Mean = \(429 / 11 = 39\)

### Step 3: Calculate the Median
The median is the middle value of the arranged data. Since we have an odd number of observations (11), the median is the value at position \( (n + 1) / 2 \).

1. **Position of Median:**
- \( (11 + 1) / 2 = 6\)

2. **6th Value in Arranged Data:**
- The 6th value is 15.

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

1. **Frequency of Each Score:**
- 6: 1 time
- 8: 1 time
- 10: 2 times
- 15: 3 times
- 50: 1 time
- 80: 1 time
- 100: 1 time
- 120: 1 time

2. **Most Frequent Score:**
- The score 15 appears 3 times, which is more than any other score.

### Step 5: Summary of Results
- **Mean:** 39
- **Median:** 15
- **Mode:** 15

### Step 6: Comparison of Mean, Median, and Mode
- The mean (39) is not the same as the median (15) and mode (15).

### Final Answer:
- Mean: 39
- Median: 15
- Mode: 15
- Are they the same? **No**

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