The measure of central tendency of a statistical data which takes into account all the data is
(i) mean
(ii) median
(iii) mode
(iv) range

Options

A. mean
B. median
C. mode
D. range

Answer

To solve the question, we need to identify which measure of central tendency takes into account all the data points in a statistical dataset. Let's analyze each option step by step.

### Step 1: Understand the Measures of Central Tendency

1. **Mean**: The mean is calculated by summing all the data points and dividing by the number of observations. This means it considers every single data point in the dataset.

2. **Median**: The median is the middle value when the data points are arranged in ascending or descending order. It only considers the middle values and does not account for all data points.

3. **Mode**: The mode is the value that appears most frequently in the dataset. It only takes into account the most common value, ignoring other data points.

4. **Range**: The range is the difference between the highest and lowest values in the dataset. It does not consider individual data points but rather just the extremes.

### Step 2: Analyze Each Option

- **Option (i) Mean**: As explained, the mean includes all data points in its calculation.
- **Option (ii) Median**: Only considers the middle values, not all data.
- **Option (iii) Mode**: Only considers the most frequent value, not all data.
- **Option (iv) Range**: Only considers the highest and lowest values, not all data.

### Step 3: Conclusion

From the analysis, we can conclude that the measure of central tendency that takes into account all the data is:

**Answer: (i) Mean**

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