The correct table to record their heights is Table A, with the following categories:
Height (cm) | Tally
--------------|-------
140-150 | *****
150-160 | *********
160-170 | ********
170-180 | **
Table A is a frequency distribution table that groups the data into intervals or classes, and records the frequency or number of times each interval occurs. It uses tallies to visually represent the frequency, which is useful for quick visual analysis. This table also covers the full range of data, and the intervals are mutually exclusive and collectively exhaustive.
The other tables are not suitable because they have some limitations:
Table B is a frequency distribution table that uses non-overlapping intervals but it does not include all the data, as there are some values between 151 and 154 that are not covered by any interval. This table is not mutually exclusive and collectively exhaustive.
Height (cm) | Tally | Frequency
--------------|--------|---------
140-149 | ***** | 5
150-159 | ******** | 8
160-169 | ******** | 8
170-179 | ** | 2
Table C is a frequency distribution table that uses non-overlapping intervals, but the intervals are not of equal size. This table is also not mutually exclusive and collectively exhaustive.
Height (cm) | Tally | Frequency
--------------|-------|---------
145-149 | ** | 2
150-154 | ***** | 5
155-159 | ******* | 7
160-161 | ** | 2
Table D is a frequency distribution table that uses equal-sized intervals, but some of the intervals overlap, which makes this table not mutually exclusive.
Height (cm) | Tally | Frequency
--------------|--------|---------
155-159 | ******* | 7
160-164 | **** | 4
165-169 | ** | 2
In conclusion, Table A is the most appropriate table to record the given heights.