Calculate the range, standard deviation, and interquartile range for the data set:

{-1, 0, 1, 2, -1, 0, 1, 2, -1, 0, 1, 2, 1, 1, -2}

I will be happy to critique your work on this.

To calculate the range, standard deviation, and interquartile range for the given data set, follow these steps:

1. Range:
The range is the difference between the highest and lowest values in the data set. To find the range:
- Sort the data set in ascending order: {-2, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2}
- The highest value is 2, and the lowest value is -2.
- Subtract the lowest value from the highest value: 2 - (-2) = 4

Therefore, the range for the given data set is 4.

2. Standard Deviation:
To calculate the standard deviation, you need to follow these steps:
- Find the mean (average) of the data set by adding up all the values and dividing by the total number of values.
- Subtract the mean from each value in the data set.
- Square each resulting difference.
- Find the mean of the squared differences.
- Take the square root of the mean of squared differences.

Here are the steps to calculate the standard deviation:
- Find the mean:
( -2 + (-1) + (-1) + (-1) + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 2 + 2 + 2 ) / 15 = 0.4 (rounded to one decimal place)

- Subtract the mean from each value and square the result:
(-2 - 0.4)^2 = 4.84
(-1 - 0.4)^2 = 1.96
(-1 - 0.4)^2 = 1.96
(-1 - 0.4)^2 = 1.96
(0 - 0.4)^2 = 0.16
(0 - 0.4)^2 = 0.16
(0 - 0.4)^2 = 0.16
(1 - 0.4)^2 = 0.36
(1 - 0.4)^2 = 0.36
(1 - 0.4)^2 = 0.36
(1 - 0.4)^2 = 0.36
(2 - 0.4)^2 = 2.56
(2 - 0.4)^2 = 2.56
(2 - 0.4)^2 = 2.56

- Find the mean of the squared differences:
(4.84 + 1.96 + 1.96 + 1.96 + 0.16 + 0.16 + 0.16 + 0.36 + 0.36 + 0.36 + 0.36 + 2.56 + 2.56 + 2.56) / 15 = 1.547 (rounded to three decimal places)

- Take the square root of the mean of squared differences:
√1.547 = 1.243 (rounded to three decimal places)

Therefore, the standard deviation for the given data set is approximately 1.243.

3. Interquartile Range (IQR):
To calculate the interquartile range, follow these steps:
- Sort the data set in ascending order: {-2, -1, -1, -1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2}
- Find the median of the lower half of the data set, known as Q1. If there are an odd number of values, ignore the median value. If there are an even number of values, take the average of the two middle values.
- Find the median of the upper half of the data set, known as Q3. If there are an odd number of values, ignore the median value. If there are an even number of values, take the average of the two middle values.
- Subtract Q1 from Q3 to find the interquartile range.

Here are the steps to calculate the interquartile range:
- Q1: Median of the lower half of the data set: -1
- Q3: Median of the upper half of the data set: 1

- Subtract Q1 from Q3: 1 - (-1) = 2

Therefore, the interquartile range for the given data set is 2.