Question

Teach me how to draw a box snd whisker plot

Answer 1

To draw a box-and-whisker plot, you need to arrange the data in ascending order, find the median, first quartile, and third quartile, calculate the interquartile range, mark the minimum and maximum values, and identify potential outliers. For the given data set, you would arrange the values, find the median, Q1, Q3, calculate IQR, mark the minimum and maximum values, and identify potential outliers. Then, you can construct the plot.

Step-by-step explanation:

To draw a box-and-whisker plot, you need to follow these steps:

Arrange the data values in ascending order.

Find the median (middle value) of the data set. This will be the line inside the box.

Find the first quartile (Q1), which is the median of the lower half of the data. This will mark the left end of the box.

Find the third quartile (Q3), which is the median of the upper half of the data. This will mark the right end of the box.

Calculate the interquartile range (IQR), which is the difference between Q3 and Q1.

Mark the minimum and maximum values as the endpoints of the whiskers, unless there are outliers.

Identify any potential outliers by using the formula Q1 - 1.5(IQR) for the lower fence and Q3 + 1.5(IQR) for the upper fence. Any data values outside these fences are potential outliers.

For the given data set: 10, 10, 10, 15, 35, 75, 90, 95, 100, 175, 420, 490, 515, 515, 790, the steps would be:

Arrange the data in ascending order: 10, 10, 10, 15, 35, 75, 90, 95, 100, 175, 420, 490, 515, 515, 790.

Find the median: (90 + 95) ÷ 2 = 92.5.

Find Q1: (15 + 35) ÷ 2 = 25.

Find Q3: (515 + 515) ÷ 2 = 515.

Calculate IQR: Q3 - Q1 = 515 - 25 = 490.

Mark the minimum and maximum values: 10 (minimum) and 790 (maximum).

Identify potential outliers: Lower fence = Q1 - 1.5(IQR) = 25 - 1.5(490) = -722.5 and upper fence = Q3 + 1.5(IQR) = 515 + 1.5(490) = 1227.5. There are no potential outliers in this data set.

Using these steps, you can construct a box-and-whisker plot for the given data set.

Answer 2

To create a box-and-whisker plot, we start by ordering our data (that is, putting the values) in numerical order, if they aren't ordered already. Then we find the median of our data. The median divides the data into two halves. To divide the data into quarters, we then find the medians of these two halves.