Let's work through each part of the question to find the mean, median, and mode for the data set:
$32, 63, 58, 79, 51, 36, 30, 60, 62, 54$

Part 1: Mean

To calculate the mean (average), we sum all the numbers and divide by the total number of values.

$\text{Sum} = 32 + 63 + 58 + 79 + 51 + 36 + 30 + 60 + 62 + 54 = 525$ The number of values is 10.

$\text{Mean} = \frac{525}{10} = 52.5$ So, the mean is 52.5 (Answer A).

Part 2: Median

To find the median, we need to arrange the data in ascending order: $30, 32, 36, 51, 54, 58, 60, 62, 63, 79$

The median is the middle value in an ordered data set. Since there are 10 values (an even number), the median is the average of the 5th and 6th values:

$\text{Median} = \frac{54 + 58}{2} = \frac{112}{2} = 56$ So, the median is 56 (Answer A).

Part 3: Mode

The mode is the number that appears most frequently. Since each value in the data set occurs only once, there is no mode.

So, the mode is there is no mode (Answer B).

Summary:

• Mean: 52.5 (Part 1, Answer A)
• Median: 56 (Part 2, Answer A)
• Mode: There is no mode (Part 3, Answer B)

Would you like any further details or explanations?

Here are 5 related questions you might find interesting:

1. How is the median affected if an additional value is added to the data set?
2. What happens to the mean if you increase one value significantly?
3. Can a data set have more than one mode? If yes, how is it determined?
4. How do you calculate the range of a data set?
5. What is the effect of an outlier on the mean and median?

Tip: The median is less sensitive to extreme values (outliers) than the mean, which can be greatly affected by them.