Heights of 25 children (in cm) in a school are as given below:168, 165, 163, 160, 163, 161, 162, 164, 163, 162, 164, 163, 160, 163, 163, 164, 163, 160, 165, 163, 162 What is the mode of heights?

Answer

To find the mode of the heights of the 25 children, we will follow these steps:

### Step 1: Organize the Data
First, we need to list the heights of the children clearly:
- Heights: 168, 165, 163, 160, 163, 161, 162, 164, 163, 162, 164, 163, 160, 163, 163, 164, 163, 160, 165, 163, 162

### Step 2: Create a Frequency Distribution Table
Next, we will create a frequency distribution table to count how many times each height occurs.

| Height (cm) | Tally Marks | Frequency |
|-------------|-------------|-----------|
| 160 | ||| | 3 |
| 161 | | | 1 |
| 162 | ||| | 3 |
| 163 | |||||||||||| | 10 |
| 164 | ||| | 3 |
| 165 | ||| | 3 |
| 166 | | 0 |
| 167 | | 0 |
| 168 | | | 1 |

### Step 3: Count the Frequencies
Now we will count the frequency of each height:
- 160 occurs 3 times
- 161 occurs 1 time
- 162 occurs 3 times
- 163 occurs 10 times
- 164 occurs 3 times
- 165 occurs 3 times
- 166 occurs 0 times
- 167 occurs 0 times
- 168 occurs 1 time

### Step 4: Identify the Mode
The mode is the height that appears the most frequently. From our table, we can see:
- 163 occurs 10 times, which is more than any other height.

### Conclusion
Thus, the mode of the heights is **163 cm**.

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