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
What can you conclude about their heights from the table?

Answer

To analyze the heights of the 50 students, we will first organize the data into a frequency distribution table. This will help us visualize the data and draw conclusions about the heights.

### Step 1: Organize the Data
We will create a frequency distribution table by grouping the heights into intervals.

**Height Intervals and Frequency:**
- 150 - 155 cm: Count the heights in this range.
- 156 - 160 cm: Count the heights in this range.
- 161 - 165 cm: Count the heights in this range.
- 166 - 170 cm: Count the heights in this range.
- 171 - 175 cm: Count the heights in this range.

### Step 2: Count the Frequencies
Now, we will count how many students fall into each height interval.

- **150 - 155 cm:** 12 students (150, 150, 154, 154, 154, 153, 153, 154, 154, 152, 153, 154)
- **156 - 160 cm:** 9 students (158, 158, 156, 156, 158, 159, 159, 159, 160)
- **161 - 165 cm:** 14 students (161, 161, 161, 161, 162, 162, 162, 162, 165, 165, 165, 165, 164, 164)
- **166 - 170 cm:** 10 students (168, 168, 168, 170, 170, 170, 170, 165, 165, 169)
- **171 - 175 cm:** 5 students (171, 172, 173)

### Step 3: Create the Frequency Distribution Table
Now, we will summarize the data in a table format.

| Height Interval (cm) | Frequency |
|-----------------------|-----------|
| 150 - 155 | 12 |
| 156 - 160 | 9 |
| 161 - 165 | 14 |
| 166 - 170 | 10 |
| 171 - 175 | 5 |
| **Total** | **50** |

### Step 4: Analyze the Data
From the frequency distribution table, we can see:
- The highest frequency is in the interval 161 - 165 cm, which has 14 students.
- The second highest frequency is in the interval 150 - 155 cm, with 12 students.
- The majority of students (35 out of 50) are below 165 cm.

### Conclusion
Based on the analysis, we can conclude that:
- More than 50% of the students have heights less than 165 cm.
- The majority of students are concentrated in the height range of 150 - 165 cm.