Let’s break down and solve the questions based on the data provided in the image. The data set contains these values for the number of transactions:
59, 72, 68, 75, 52, 91, 99, 93.

(a) Find the median:

1. Arrange the data in ascending order:
   $52, 59, 68, 72, 75, 91, 93, 99$
2. Since there are 8 values (even number), the median is the average of the 4th and 5th values.
   $\text{Median} = \frac{72 + 75}{2} = \frac{147}{2} = 73.5$

Answer for (a): $73.5$

(b) Find the mean:

1. Add all the values:
   $52 + 59 + 68 + 72 + 75 + 91 + 93 + 99 = 609$
2. Divide by the total number of values (8):
   $\text{Mean} = \frac{609}{8} = 76.1$

Answer for (b): $76.1$

(c) Find the modes:

1. Check the frequency of each value in the data:
   $52, 59, 68, 72, 75, 91, 93, 99$
   All values appear once.
2. Since no value repeats, the data set has zero modes.

Answer for (c): Zero modes

Final Answers:

(a) Median: 73.5
(b) Mean: 76.1
(c) Modes: Zero modes

Would you like additional clarification on any step?

Related Questions:

1. How is the mean calculated for grouped or ungrouped data?
2. Why is the median sometimes a better measure of central tendency than the mean?
3. What happens if there are multiple modes in a data set?
4. How would outliers affect the mean in this data set?
5. Can a data set with zero modes still have a high standard deviation?

Tip:

For small data sets, always double-check by ordering the numbers first—it simplifies calculations for both mean and median!