Question

Determine the minimum, maximum, and quartile values. Remember, the first step is to put the values in order from least to greatest.

{-1,-1.35,-0.95,0.5,0,-0.75,0.25}

Answer 1

The minimum value is -1.35, the first quartile is -0.975, the median is 0, the third quartile is 0.375, and the maximum value is 0.5. The interquartile range (IQR) is 1.35.

Step-by-step explanation:

To address the student's query, we'll order the data points and determine the minimum, maximum, quartiles, and percentiles.

1. Firstly, order the data from least to greatest:
   {-1.35, -1, -0.95, -0.75, 0, 0.25, 0.5}.
2. The minimum value is -1.35.
3. To calculate the median (also known as the second quartile Q2), which is the middle value in the ordered set, we find that 0 is the median since it is the fourth value of the seven.
4. The first quartile (Q1), or the 25th percentile, is the median of the lower half (not including the median). In this case, it is the average of -1 and -0.95, giving us -0.975 as Q1.
5. The third quartile (Q3), or 75th percentile, is the median of the upper half (again, not including the median). For this data, it is the average of 0.25 and 0.5, resulting in 0.375 as Q3.
6. The maximum value is 0.5.
7. The interquartile range (IQR) is Q3 - Q1, which is 0.375 - (-0.975) = 1.35.
8. Percentiles such as the 37th percentile and the 63rd percentile need interpolation since our dataset is small. However, we can approximate the 37th percentile to be around -0.75 and the 63rd percentile to be around 0.25, as those are the closest values to those percentages in the ordered list.

A box plot could be constructed with this information to visually represent the spread and central tendency of the dataset.