The heights of 50 students, measured to the nearest centimetres, have been found to be as follows: 161 150 154 165 168 161 154 162 150 151
162 164 171 165 158 154 156 172 160 170
153 159 161 170 162 165 166 168 165 164
154 152 153 156 158 162 160 161 173 166
161 159 162 167 168 159 158 153 154 159
Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160-165, 165-170, etc.

Answer

To represent the given heights of 50 students in a grouped frequency distribution table, we will follow these steps:

### Step 1: Determine the Class Intervals
We need to create class intervals based on the given data. The lowest height is 150 cm and the highest is 172 cm. We will use class intervals of 5 cm starting from 150 cm.

- Class intervals will be:
- 150 - 155
- 155 - 160
- 160 - 165
- 165 - 170
- 170 - 175

### Step 2: Tally the Frequencies
Next, we will count how many students fall into each class interval.

1. **150 - 155**: Count the heights in this range.
- Heights: 150, 150, 154, 154, 154, 153, 153, 154, 154, 153
- Frequency: 10

2. **155 - 160**: Count the heights in this range.
- Heights: 158, 156, 158, 158, 156, 156, 159, 159
- Frequency: 8

3. **160 - 165**: Count the heights in this range.
- Heights: 161, 161, 162, 162, 162, 164, 161, 161, 162, 162, 165, 165, 165
- Frequency: 13

4. **165 - 170**: Count the heights in this range.
- Heights: 168, 168, 165, 165, 166, 167, 170, 170, 170
- Frequency: 10

5. **170 - 175**: Count the heights in this range.
- Heights: 171, 172, 173
- Frequency: 5

### Step 3: Create the Frequency Distribution Table
Now we can compile our findings into a frequency distribution table.

| Class Interval | Frequency |
|----------------|-----------|
| 150 - 155 | 10 |
| 155 - 160 | 8 |
| 160 - 165 | 13 |
| 165 - 170 | 10 |
| 170 - 175 | 5 |
| **Total** | **50** |

### Step 4: Verify the Total Frequency
Finally, we will check if the total frequency sums up to 50, which it does.