(a) Data set: 12, 24, 13, 21, 13, 20, 15, 18, 15, 16

1. Mean: The mean is calculated by summing all the values and dividing by the number of values.

   $\text{Mean} = \frac{12 + 24 + 13 + 21 + 13 + 20 + 15 + 18 + 15 + 16}{10} = \frac{167}{10} = 16.7$

2. Median: The median is the middle value when the data is ordered. First, we arrange the numbers in ascending order:

   12, 13, 13, 15, 15, 16, 18, 20, 21, 24

   Since there are 10 numbers, the median is the average of the 5th and 6th values:

   $\text{Median} = \frac{15 + 16}{2} = \frac{31}{2} = 15.5$

3. Mode: The mode is the most frequent value in the data. Here, both 13 and 15 appear twice, so the data is bimodal:

   $\text{Mode} = 13 \text{ and } 15$

(b) Data set: 22, 43, 26, 14, 2, 5, 54, 43, 63, 24, 52, 5

1. Mean: $\text{Mean} = \frac{22 + 43 + 26 + 14 + 2 + 5 + 54 + 43 + 63 + 24 + 52 + 5}{12} = \frac{353}{12} \approx 29.42$

2. Median: First, we arrange the numbers in ascending order:

   2, 5, 5, 14, 22, 24, 26, 43, 43, 52, 54, 63

   Since there are 12 numbers, the median is the average of the 6th and 7th values:

   $\text{Median} = \frac{24 + 26}{2} = \frac{50}{2} = 25$

3. Mode: The mode is the most frequent value in the data. Both 5 and 43 appear twice, so this data set is also bimodal:

   $\text{Mode} = 5 \text{ and } 43$

Summary:

• (a) Mean = 16.7, Median = 15.5, Mode = 13 and 15
• (b) Mean = 29.42, Median = 25, Mode = 5 and 43

Would you like more details or have any questions?

Related Questions:

1. How do you compute the mean when there are repeated values in a data set?
2. What is the difference between median and mode?
3. How can a data set have more than one mode?
4. What happens to the mean if an extreme value is added to the data set?
5. Why is the median often preferred over the mean for skewed data?

Tip: The mode can be used for both numerical and categorical data, unlike the mean and median which are only for numerical data.