Profits in '000:

- The given data represents the profits (in thousands) of a certain number of firms.
- The data is divided into different profit ranges, with the lowest range being "less than 10" and the highest range being "50-59".
- The number of firms corresponding to each profit range is also provided.

Calculating the third quartile:

- The third quartile is a measure of central tendency that divides the data into lower and upper halves. It represents the value below which 75% of the data falls.
- To calculate the third quartile for the given data, we need to find the cumulative frequency at which 75% of the data falls.
- The cumulative frequency is the sum of the frequencies up to a certain point.

Cumulative Frequency:

- To calculate the cumulative frequency, we start with the frequency of the first range and add it to the frequencies of subsequent ranges.
- For example, for the range "less than 10", the cumulative frequency is 5 because there are 5 firms in that range.
- Similarly, for the range "10-19", the cumulative frequency is 5 + 18 = 23, as there are 18 firms in that range in addition to the previous 5.

Calculating the third quartile (continued):

- To find the cumulative frequency at which 75% of the data falls, we multiply the total number of firms by 75% (or 0.75).
- In this case, the total number of firms is not given, so we have to use a formula to estimate it.
- The formula is: Total number of firms = (Cumulative frequency at the third quartile) / (Percentage corresponding to the third quartile)
- In our case, the cumulative frequency at the third quartile is 75% of the total number of firms, so we can rewrite the formula as: Total number of firms = (Cumulative frequency at the third quartile) / 0.75

Calculating the 65th percentile:

- The 65th percentile is a measure of central tendency that represents the value below which 65% of the data falls.
- To calculate the 65th percentile for the given data, we need to find the cumulative frequency at which 65% of the data falls.
- We can use the same approach as for calculating the third quartile, but with a different percentage (65% instead of 75%).

Explanation:

- To provide a detailed explanation of the calculations for the third quartile and 65th percentile, we need the actual cumulative frequencies for each profit range.
- The given data only provides the profit ranges and the number of firms, but not the cumulative frequencies.
- Without the cumulative frequencies, it is not possible to calculate the third quartile and 65th percentile accurately.
- Therefore, we need additional information or data to proceed with the calculations and provide a detailed explanation.