Identify the minimum, first quartile, median, third quartile, and maximum of the data set. Then make a box-and-whisker plot of the data set. file sizes (megabytes)229,246,173,159, 77,129,128 The minimum is
77, the first quartile is 128, the median is 159, the third quartile is 229, and the maximum is 246.
To make a box-and-whisker plot, draw a number line and mark the minimum, first quartile, median, third quartile, and maximum. Then draw a box spanning from the first quartile to the third quartile and draw whiskers from the box to the minimum and maximum.
The box-and-whisker plot for this data set would look like:
```
|
--+------------
77|___________
| |
| |
128|-----------
| |
159|-----------|
| |
| |
229|___________|
| |
246| |
|
```
To identify the minimum, first quartile, median, third quartile, and maximum of the given dataset, I will first sort the data in ascending order:
77, 128, 129, 159, 173, 229, 246
Now, I will calculate the quartiles:
1. Minimum: The smallest value in the dataset is 77.
2. First quartile (Q1): The median of the lower half of the dataset. In this case, it is the median of the first 3 values, which are 77, 128, and 129. So, Q1 = 128.
3. Median (Q2): The middle value of the dataset. Since we have 7 data points, the median is the value at the (7+1)/2 = 4th position. So, the median is 159.
4. Third quartile (Q3): The median of the upper half of the dataset. Considering the values 173, 229, and 246, the median is (173+229)/2 = 201.
5. Maximum: The largest value in the dataset is 246.
Now, let's create a box-and-whisker plot of the data:
```
--|-------|-------|--------|--------|-----|------|--
77 128 129 159 173 229 246
```
In this plot, the line in the middle represents the median (159). The box represents the interquartile range (from Q1 to Q3), and the whiskers represent the minimum (77) and maximum (246) values.