2.1 Data Analysis With Graphs

Statistics: the gathering, organization, analysis, and presentation of numerical information

Raw data: the unprocessed information collected for a study

Variable: the quantity being measured
1) continuous variable: any value within a given range
2) discrete variable: certain separate values (often integers)

Frequency tables/diagrams: shows an overview of the distrubution of values of the variables and reveal trends in the data

Bar graph: a chart or diagram that represents quantities with horizontal or vertical bars whose lengths are proportional to the quantities. (eg. hair colour, citizenship)

Histogram: a special form of bar graph in which the areas of the bars are proportional to the frequencies of the values of the variable.
- the bars in a histogram are connected ( continuous range of values )
- histograms are used for variables whose values can be arranged in numerical order, especially continuous variables (eg. time, weight, temperature)

Frequency Polygon: similar to a histogram or bar graph. But the only difference is that frequencies versus variable values have to be plotted and then join the points with straight lines.

Example 1: Frequency table
Sum Tally Frequency
2 4 4
3 2 2
4 3 3
5 9 9
6 8 8
7 5 5
8 6 6
9 5 5
10 4 4
11 3 3
12 1 1

intervals: a set of all numbers between two given numbers.

Range: the difference between the highest and lowest values in a set of data.

Relative-frequency table/diagram: the frequency of a data group as a fraction or percent of the whole data set.

Example 2: Relative-frequency table
Score Midpoint Tally Frequency Relative Frequency
34.5-39.5 37 1 1 0.033
39.5-44.5 42 1 1 0.033
44.5-49.5 47 0 0 0
49.5-54.5 52 1 1 0.033
54.5-59.5 57 2 2 0.067
59.5-64.5 62 4 4 0.133
64.5-69.5 67 4 4 0.133
69.5-74.5 72 6 6 0.200
74.5-79.5 77 4 4 0.133
79.5-84.5 82 3 3 0.100
84.5-89.5 87 2 2 0.067
89.5-94.5 92 1 1 0.033
94.5-99.5 97 1 1 0.033

Categorial data: data that can be sorted or divided by type rather than by numerical values.

Circle graph (or pie charts): a graph that represents quantities with segments of a circle that are proportional to the quantities.

Pictographs: a chart or diagram that represents quantities with symbols.