The mean, median and mode of given data of scores are 21, 23 and 22 respectively. If 3 is added to each score. What are the new values of mean, median and mode respectively.

Options

A. 21, 23, 24
B. 24, 26, 25
C. 24, 23, 22
D. 23, 21, 24

Answer

To find the new values of mean, median, and mode after adding 3 to each score, we can follow these steps:

### Step 1: Understand the given values
The original mean, median, and mode are given as:
- Mean (x̄) = 21
- Median = 23
- Mode = 22

### Step 2: Calculate the new mean
When we add a constant (in this case, 3) to each score, the new mean can be calculated by simply adding that constant to the original mean.

New Mean (ȳ) = Original Mean + Constant
\[ ȳ = 21 + 3 = 24 \]

### Step 3: Calculate the new median
The median is the middle value of the ordered data. Since we are adding the same constant to each score, the order of the data does not change. Therefore, we can find the new median by adding the constant to the original median.

New Median = Original Median + Constant
\[ \text{New Median} = 23 + 3 = 26 \]

### Step 4: Calculate the new mode
The mode is the value that appears most frequently in the data set. Since we are adding the same constant to each score, the mode will also increase by that constant.

New Mode = Original Mode + Constant
\[ \text{New Mode} = 22 + 3 = 25 \]

### Final Results
After adding 3 to each score, the new values are:
- New Mean = 24
- New Median = 26
- New Mode = 25

### Summary
Thus, the new values of mean, median, and mode are 24, 26, and 25, respectively.

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