1. By the end of this lesson you will be able to explain/calculate the following: 1. Histogram 2. Frequency Polygons

2. Graphing Data are displayed with the aid of graphs so the information can be easily understood and evaluated. Graphs also enable future trends or comparisons to be made.

3. Key Features Key features of graphs include: 1.a bold and appropriate title 2.clearly-labelled and evenly scaled axes 3.an attractive use of line, shading and colour 4.a key or legend for any symbols used, with roundings noted 5.a source of data which clearly identifies the origin of the information. You should already know various types of graphs. histogramfrequency polygon The most important statistical displays are the histogram and frequency polygon

4. Worked Example

7. Grouped Data Where there is a large amount of data or the data are spread over a wide range, it is convenient to group the scores into class intervals. The choice for the size of the class intervals should lead to between 5 and 10 groups being formed.

8. Grouped Data Class intervals are set so that each score belongs to one group only. When presenting grouped data graphically, the horizontal (score) axis may be labelled with either: the class interval, or the centre score (midpoint) of each class interval.

9. Worked Example

12. 10 - 14 3 6 17 2

14. Describing spread of data: Spread The spread of a distribution refers to the variability of the data. If the observations cover a wide range, the spread is larger. If the observations are clustered around a single value, the spread is smaller.range In the figure on the left, data values range from 3 to 7; whereas in the figure on the right, values range from 1 to 9. The figure on the right is more variable, so it has the greater spread.

15. Describing the distribution of graphs: Shape: The shape of a distribution is described by the following characteristics. Symmetry: When it is graphed, a symmetric distribution can be divided at the center so that each half is a mirror image of the other. Number of peaks: Distributions can have few or many peaks. Distributions with one clear peak are called unimodal, and distributions with two clear peaks are called bimodal. When a symmetric distribution has a single peak at the center, it is referred to as bell-shaped. Skewness: When they are displayed graphically, some distributions have many more observations on one side of the graph than the other. Distributions with most of their observations on the left (toward lower values) are said to be skewed right; and distributions with most of their observations on the right (toward higher values) are said to be skewed left. Uniform: When the observations in a set of data are equally spread across the range of the distribution, the distribution is called a uniform distribution. A uniform distribution has no clear peaks.

16. Bimodal distribution: A histogram is unimodal if there is one hump, bimodal if there are two humps and multimodal if there are many humps. Unimodal, Symmetric, Nonskewed

17. Nonsymmetric distribution A nonsymmetric histogram is called skewed if it is not symmetric. If the upper tail is longer than the lower tail then it is positively skewed. If the upper tail is shorter than it is negatively skewed.

18. Ununusal features with data: Gaps:refer to areas of a distribution where there are no observations. The first figure below has a gap; there are no observations in the middle of the distribution. Outliers: extreme values that differ greatly from the other observations. The second figure below illustrates a distribution with an outlier. Except for one lonely observation (the outlier on the extreme right), all of the observations fall between 0 and 4.

19. Histogram Recap: Histograms are used to show the frequency of data. Very similar to bar graphs, but use intervals on the X axis. Bars do touch. Histograms have a title. Histograms have two axes which are labeled.