Fundamentals of Math - old

Fundamentals of Mathematics

count how many items are in each bin. Finally, draw a rectangle on the graph that corresponds to the percentage of the total that bin fills.

Example 6.5

Directions: Using the data from Table 6.1 create a histogram that showcases the sodium to potassium ratio in patients.

Begin by determining the number of bins you want to use. Notice the minimum value in the dataset is 6.27 and the maximum is 38.25 giving us a total range of 31.98. From here it is pure opinion on the number of bins we should use, but in this example, we will opt for 8 – each bin with a range of 5.

Bin 1 (0,5]

Bin 2 (5,10]

Bin 3

Bin 4

Bin 5

Bin 6

Bin 7

Bin 8

Intervals Frequency

(10,15] (15,25] (20,25] (25,30] (30,35] (35,40)

0

38

71

44

16

19

9

3

A formal study in descriptive statistics will focus in more extensive detail on how to interpret histograms. For now, we will focus on the big picture. Take note of the shape of the histogram. There is one large peak between (10,15], and then the graph trails off to the right. The highest peak of the graph tells us where most of the data lie. Meaning most of the patients in the dataset have a sodium to

potassium blood concentration ratio between 5 and 10 units. The other rectangles we see to the right of this are much shorter and continue outward from our peak range for a while. This is indicative of possible outliers (values that occurred in the dataset, but were not likely to occur). Also, given that the ratio is sodium to potassium, then we could logically deduce to obtain a value 25 or higher, the sodium blood concentration level must be much larger than the potassium concentration level. We would need to consult with a medical expert to interpret the clinical significance of these findings. 6.6 Scatter Plots A scatterplot is a type of graph that shows the relationship between two numerical variables. Each member of the dataset gets plotted as a point whose ( , ) coordinates relate to its values for the two variables. Similar to that of a line graph, but unlike a line graph, the data points are never connected. Statisticians will study how these points lie on a graph and draw conclusions based on any discernable shapes or patterns they see.

©2019 Achieve Page 93 of 127