Section 2-3 Histograms

VISUALIZING DATA In this section, we will learn various ways that data can be visualized. The goal is not simply to construct graphs and diagrams – but rather to learn something about the data and understand the nature of their distributions.

HISTOGRAMS A histogram is a bar graph in which the horizontal scale represents classes of data values and the vertical scale represents frequencies (or relative frequencies). The heights of the bars correspond to the frequency values, and the bars are drawn adjacent to each other without gaps.

QWERTY WORD RATING FREQUENCY HISTOGRAM 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency

QWERTY WORD RATING RELATIVE FREQUENCY HISTOGRAM 0 - 2 38.5% 3 - 5 26.9% 6 - 8 28.8% 9 - 11 3.8% 12 - 14 1.9% Rating Relative Frequency

HISTOGRAM AND RELATIVE FREQUENCY HISTOGRAM

DRAWING A FREQUENCY HISTOGRAM FROM RAW DATA ON THE TI-83/84 Press STAT; select 1:Edit…. Enter your data values in L1. (Note: You could enter them in a different list.) Press WINDOW. Set Xmin to the lower class boundary of the first class; set Xmax to the upper class boundary of the last class; and set Xscl to the class width. (Note: You may need to set Ymin and Ymax to see the histogram.) Press 2ND, Y= (for STATPLOT). Select 1:Plot1. Turn the plot ON. For Type, select the histogram (last one on first row). For Xlist, enter L1 by pressing 2ND, 1. For Freq, enter the number 1.

DRAWING A FREQUENCY HISTOGRAM FROM A FREQUENCY DISTRIBUTION ON THE TI-83/84 Compute the midpoint of each class. Press STAT; select 1:Edit…. Enter the midpoints in L1 and the frequency for the class in L2. Press WINDOW. Set Xmin to the lower class boundary of the first class; set Xmax to the upper class boundary of the last class; and set Xscl to the class width. (Note: You may need to set Ymin and Ymax to see the histogram.) Press 2ND, Y= (for STATPLOT). Select 1:Plot1. Turn the plot ON. For Type, select the histogram (last one on first row). For Xlist, enter L1 by pressing 2ND, 1. For Freq, enter L2 by pressing 2ND, 2.

FREQUENCY POLYGON A frequency polygon uses line segments connected to points above class midpoint values.

OGIVE An ogive is a line graph that depicts cumulative frequencies.

DOTPLOT A dotplot consists of a graph in which each data value is plotted as a point (or dot) along a scale of values. Dots representing equal values are stacked.

STEM-AND-LEAF PLOTS A stem-and-leaf plot represents data by separating each value into two parts: the stem (such as the left most digit) and the leaf (such as the right most digit). Stem Leaves Raw Data (Test Grades) 67 72 85 75 89 89 88 90 99 100 6 7 8 9 10 7 2 5 5 8 9 9 0 9

PARETO CHARTS A Pareto chart is a bar graph for qualitative data, with the bars arranged in order according to frequencies.

EXAMPLE OF A PARETO CHART 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 Accidental Deaths by Type Frequency Falls Fire Poison Drowning Firearms Motor Vehicle Ingestion of food or object

PIE CHART Accidental Deaths by Type Firearms (1400. 1.9%) (1400. 1.9%) Ingestion of food or object (2900. 3.9% Fire (4200. 5.6%) Motor vehicle (43,500. 57.8%) Drowning (4600. 6.1%) Poison (6400. 8.5%) Falls (12,200. 16.2%) Accidental Deaths by Type