Plots and Data Analysis
There are two types of data: categorical and numerical.
Categorical data: can be sorted into groups or categories
Numerical data: can be measured
For example, breeds of dogs would be categorical and weights of dogs would be numerical.
A line plot shows the frequency of data on a number line with marks used to show data points.
In the line plot to the right, how many distances of 24 meters are there? How many total data points are there?
There are 4 dots above the number 24, so there are 4 distances of 24 meters.
There are 17 total dots, which means that there are 17 total data points.
Stem and Leaf Plots
Each value must first be separated into a stem and a leaf; for example, two-digit numbers can be separated into tens as the stems and ones as the leaves
The stems are listed vertically in ascending order (least to greatest) with a line to their right
The leaves are listed horizontally next to its corresponding stem, also from least to greatest
Every value is recorded, regardless of the number of repeats
No stem can be skipped; for example, if there is no data for a stem, it should be shown with no leaves
Once we have data, we need to analyze it. We can do this by finding values such as the mean, median, mode, and range.
A measure of center is a value at the center or middle of a data set. Mean, median, and mode are measures of center.
Mean: arithmetic average; add all of the data points and then divide by the number of data points
Median: the middle value of a data set in ascending order
Odd number of data points: the median is the middle value
Even number of data points, the median is the average of the two middle values
Mode: the piece of data that occurs most frequently; there may be one, more than one, or no mode in a data set
Range: the spread of a set of data; the difference between the greatest and least values in the data set
Suppose you are trying to analyze the heights in inches of some of your classmates. The heights are 58, 59, 58, 60, 65, 57, 60, and 53 inches. Find the mean, median, mode, and range.
The easiest way to do this is to first put the data points in ascending order.
53, 57, 58, 58, 59, 60, 60, 65
The mean is the sum of the data divided by the number of data points.
(53 + 57 + 58 + 58 + 59 + 60 + 60 + 65) / 8 = 58.75 inches
The median is the data point in the middle. There are an even number of data points, so we have to take the average of the middle two data points, which are 58 and 59.
(58 + 59) / 2 = 58.5 inches
The mode is the data point that occurs the most often. There are two data points that occur twice, 58 and 60, so those are our two modes.
The range is the greatest data point minus the smallest data point. 65 - 53 = 12 inches.
Don’t forget units!