## Data, Graphing, and Probability

Organizing Data
Collecting, organizing, reporting, and interpreting data are activities of great importance in many areas of life. To interpret data meaningfully, it is important to present data in an easily understood form.

There are many forms in which data can be organized and presented. If a child is collecting data in order to find which of three activities is the favorite of twenty children, a tally chart can be used to organize the data. To simplify counting the tally marks, it is customary to cross each group of four marks with another tally mark to form a cohesive group of five tally marks.

Pictographs
A pictograph represents data with pictures. It is often used when data are multiples of a number. For example, pictures of leopards can be used to show how many leopards are in different zoos. The title tells what the graph is about, and the labels tell what information is shown. A key is used to show how many leopards each picture represents.

Bar Graphs
A bar graph is used to display data when the data can be counted and you want to make comparisons. A vertical bar graph has a horizontal scale which names the items being counted. A vertical scale, at the left, shows the number counted. For example, snacks chosen by children as being their favorite may be listed along the horizontal scale. The vertical line may be numbered 0, 1, 2, 3, 4, and 5. The lengths of the bars would represent the numbers of children that chose a particular snack. On a horizontal bar graph, the locations of the scales are reversed.

Statistics
Statistics that give some indication of the “typical” number in a set of data are called measures of central tendency. Three measures of central tendency are the mean, median, and mode. The mean is the average of the set of data. The median is the middle number when the data are arranged in order. The mode is the number that occurs most often in a data set. Statistics that give an indication how the data are “spread out” are called measures of dispersion. The range of the numbers, the difference between the largest and the smallest numbers, is a measure of dispersion. At this grade level, children are introduced to the mode and range as shown on a line plot.

Probability
Probability is a branch of mathematics in which chance events are studied. An event is something that may or may not happen. The likelihood of outcomes for chance events can be predicted by using probability. For example, consider a spinner that has 8 equal sections with 2 blue, 2 red, and 4 yellow. Spin this spinner and it is most likely to land on yellow, because more of the spinner is yellow than blue or red. The spinner is equally likely to land on red as on blue, because there is an equal number of red and blue sections on the spinner. When events are equally likely, the probability of an event is equal to the number of favorable outcomes divided by the number of possible outcomes. The probability of an event can be any number from 0 through 1. It is impossible for an event with a probability of 0 to happen. An event with a probability of 1 is certain to happen.

Teaching Model 4.4: Graphing on a Coordinate Grid