Question

Now, we can map out the four groups formed from the quartiles. The first group of values contains the smallest number up to Q1; the second group includes Q1 to the median; the third set is the median to Q3; the fourth category comprises Q3 to the highest datapoint of the entire set.

Answer 1

Quartiles divide data into four equal parts, with the median (Q2) dividing the data set in half. Q1 is the median of the lower half, and Q3 is the median of the upper half. Box plots visually represent these quartiles along with the smallest and largest values in the data set.

Step-by-step explanation:

Understanding Quartiles and Box Plots in Data Sets

Quartiles are the values that divide a data set into quarters, which may or may not be part of the data set itself. The second quartile, also known as the median, cuts the data set in half. For example, in the given data set 1, 1, 2, 2, 4, 6, 6.8, 7.2, 8, 8.3, 9, 10, 10, 11.5, the median is 7. The first quartile (Q1), which is the median of the lower half excluding the median of the data set, would be 2. Conversely, the third quartile (Q3) is the median of the upper half, which is 9 in this case.

To construct a box plot, we represent these quartiles as well as the smallest and largest data values. The box plot provides a visual representation of the distribution, showing the range and the interquartile range (IQR), which is the distance between Q1 and Q3. Whiskers extend from the box to the smallest and largest values, providing a clear picture of data spread and potential outliers.

Box plots are a convenient way of graphically depicting groups of numerical data through their quartiles. By using a box plot, we can easily compare different data sets and understand key characteristics such as spread and central tendency.