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.

At the ends of the **box**, you” **find** the first quartile (the 25% mark) and the third quartile (the 75% mark). The far left of the chart (at the end of the left “whisker”) is the **minimum** (the **smallest** number in the set) and the far right is the **maximum** (the largest number in the set).

Subsequently, question is, how do you determine outliers? A point that falls outside the data set’s inner fences is classified as a minor **outlier**, while one that falls outside the outer fences is classified as a major **outlier**. To **find** the inner fences for your data set, first, multiply the interquartile range by 1.5. Then, add the result to Q3 and subtract it from Q1.

Similarly, how do you find the box and whisker plot?

The **box** in the **box plot** will show the median and the first and third quartiles. The length of the upper **whisker** is the largest value that is no greater than the third quartile plus 1.5 times the interquartile range. In this case, the third quartile plus 1.5 times IQR is 10 + 1.5*6 = 19.

How do you construct a scatter plot?

**Scatter Diagram Procedure**

- Collect pairs of data where a relationship is suspected.
- Draw a graph with the independent variable on the horizontal axis and the dependent variable on the vertical axis.
- Look at the pattern of points to see if a relationship is obvious.
- Divide points on the graph into four quadrants.

### How are quartiles calculated?

Quartiles are the values that divide a list of numbers into quarters: Put the list of numbers in order. Then cut the list into four equal parts. In this case all the quartiles are between numbers: Quartile 1 (Q1) = (4+4)/2 = 4. Quartile 2 (Q2) = (10+11)/2 = 10.5. Quartile 3 (Q3) = (14+16)/2 = 15.

### What is a box and whisker plot in math?

A box and whisker plot (sometimes called a boxplot) is a graph that presents information from a five-number summary. In a box and whisker plot: the ends of the box are the upper and lower quartiles, so the box spans the interquartile range. the median is marked by a vertical line inside the box.

### What does a box plot tell you?

A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”). It can tell you about your outliers and what their values are.

### How do you find the first quartile?

The first quartile, denoted by Q1 , is the median of the lower half of the data set. This means that about 25% of the numbers in the data set lie below Q1 and about 75% lie above Q1 . The third quartile, denoted by Q3 , is the median of the upper half of the data set.

### What is outliers in SPSS?

Outliers in statistical analyses are extreme values that do not seem to fit with the majority of a data set. SPSS is one of a number of statistical analysis software programs that can be used to interpret a data set and identify and remove outlying values.

### How do you solve a box and whisker plot problem?

Step 1: Arrange the data in ascending order. Step 2: Find the median, lower quartile and upper quartile. Step 3: Draw a number line that will include the smallest and the largest data. Step 4: Draw three vertical lines at the lower quartile (12), median (22) and the upper quartile (36), just above the number line.

### What are the five values of a box and whisker plot?

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

### What is the range of a box plot?

If you are interested in the spread of all the data, it is represented on a boxplot by the horizontal distance between the smallest value and the largest value, including any outliers. In the boxplot above, data values range from about 0 (the smallest non-outlier) to about 16 (the largest outlier), so the range is 16.

### Can median and lower quartile be the same?

Mentor: The lower quartile is the median of the first 50% of the data. And the upper quartile is the median of the last 50% of the data. If there is an even number of data points then the quartile is the average of the two middle numbers, just like when we found the median.