1. CHAPTER 37 Presentation of Data 2

2. Time Series A TIME SERIES is a set of readings taken at TIME INTERVALS. A TIME SERIES is often used to monitor progress and to show the TREND (increase or decrease) so that future performance can be predicted. A LINE GRAPH is used to display a TIME SERIES.

3. Seasonal Variation and Moving Averages SEASONAL VARIATIONS are ups and downs in the numerical values in the TIME SERIES because of the season of the year in which they are recorded. To get a better idea of the average value of the numbers under consideration in the TIME SERIES it is necessary to smooth out these SEASONAL VARIATIONS using MOVING AVERAGES. To smooth out SEASONAL VARIATION it is necessary to find the average for every four quarters moving forward one quarter at a time. These are called MOVING AVERAGES. The number of points chosen for the moving average depends on the pattern in the data eg if the pattern is repeated every 4 quarters we would use a 4-point moving average.

4. Moving Average Graphs Moving Averages are calculated in order to investigate the general TREND in a TIME SERIES. Each MOVING AVERAGE is plotted at the Mid point of the period to which it refers. When all the points have been plotted a line of best fit is drawn for the moving averages to show the general TREND.

5. Frequency Diagrams We use BARCHARTS when data can be counted and there are only a few different items of data. If there is a lot of data, or the data is continuous we draw a HISTOGRAM or FREQUENCY POLYGON. HISTOGRAMS WITH EQUAL CLASS WIDTH INTERVALS HISTOGRAMS are used to present information contained in GROUPED FREQUENCY DISTRIBUTIONS. There are no gaps between the bars of a HISTOGRAM. In a HISTOGRAM with equal class intervals the FREQUENCY is the HEIGHTS of bars. FREQUENCY POLYGONS are often used instead of histograms when we need to compare two, or more, groups of data. To draw a FREQUENCY POLYGON:  Plot the frequencies at the midpoint of each class interval  Join successive points with straight lines  To compare data, frequency polygons for different groups of data can be drawn on the same diagram.

6. Frequency Polygons - Example The following information gives the length of 30 leaves measured to the nearest millimetre. 41303931132142352634 36333111303216174136 25352421261434472240 Group the data and draw a frequency polygon ANSWER The smallest length is 11mm and the largest length is 47mm so we will group the data into class intervals 10-14, 15-19, 20-24