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

Data set: 1.48, 1.15, 1.24, 1.46, 1.31, 1.19, 0.32, 1.43, 1.39, 1.03, 0.76

1. Mean:

The mean is the average of the numbers. It's calculated by adding all the values together and dividing by the total number of values.

$\text{Mean} = \frac{1.48 + 1.15 + 1.24 + 1.46 + 1.31 + 1.19 + 0.32 + 1.43 + 1.39 + 1.03 + 0.76}{11}$

Let's compute that:

$\text{Mean} = \frac{13.76}{11} = 1.25$

2. Median:

The median is the middle number in a sorted list. First, let's arrange the data set in increasing order:

0.32, 0.76, 1.03, 1.15, 1.19, 1.24, 1.31, 1.39, 1.43, 1.46, 1.48

Since there are 11 values (an odd number), the median is the 6th value.

$\text{Median} = 1.24$

3. Midrange:

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

$\text{Midrange} = \frac{\text{Min} + \text{Max}}{2} = \frac{0.32 + 1.48}{2} = \frac{1.80}{2} = 0.90$

4. Mode:

The mode is the value that appears most frequently. Since all values occur only once, there is no mode.

$\text{Mode} = \text{None}$

Summary:

• Mean: 1.25
• Median: 1.24
• Midrange: 0.90
• Mode: None

Would you like more details or have any questions?

Here are five related questions:

1. How would you calculate the range of this data set?
2. What is the variance and standard deviation of this data set?
3. How do you interpret the difference between mean and median?
4. How is the midrange used in data analysis compared to other measures?
5. How would adding a new data point affect these values?

Tip: The median is less affected by extreme values than the mean, making it a better measure for skewed data.