Let's calculate the mean, median, midrange, and mode for the given data set:

Data Set:
0.33, 1.32, 0.69, 1.08, 0.28, 0.96, 0.77, 1.27, 1.05, 1.02, 0.34

1. Mean

The mean is calculated by summing all the numbers in the data set and then dividing by the number of elements.

$\text{Mean} = \frac{\sum \text{Data}}{\text{Number of elements}}$

$\text{Mean} = \frac{0.33 + 1.32 + 0.69 + 1.08 + 0.28 + 0.96 + 0.77 + 1.27 + 1.05 + 1.02 + 0.34}{11} = \frac{9.11}{11} \approx 0.8282$

2. Median

The median is the middle value when the data is arranged in ascending order. If there is an odd number of observations, the median is the middle number; if even, it is the average of the two middle numbers.

Ordered Data Set:
0.28, 0.33, 0.34, 0.69, 0.77, 0.96, 1.02, 1.05, 1.08, 1.27, 1.32

Since there are 11 elements (odd), the median is the 6th value:

$\text{Median} = 0.96$

3. Midrange

The midrange is calculated by finding the average of the maximum and minimum values in the data set.

$\text{Midrange} = \frac{\text{Max value} + \text{Min value}}{2}$

$\text{Midrange} = \frac{1.32 + 0.28}{2} = \frac{1.60}{2} = 0.80$

4. Mode

The mode is the value that appears most frequently in the data set.

Since all numbers occur only once, there is no mode for this data set.

Summary:

• Mean: 0.8282 (approximately)
• Median: 0.96
• Midrange: 0.80
• Mode: None

Would you like to explore any of these calculations further or have any other questions?

5 Related Questions:

1. How would the mean change if one more value were added to the data set?
2. What is the range of the data set, and how is it different from the midrange?
3. How does the median help in understanding the distribution of the data compared to the mean?
4. Can a data set have more than one mode? If so, how would you determine them?
5. How would removing the smallest and largest values affect the mean, median, and midrange?

Tip: The median is often a better measure of central tendency than the mean in a skewed distribution because it is less affected by extreme values.