TIME SERIES SCATTER DIAGRAM (SEMI AVERAGE) FOR STATISTICS GCE O LEVELS/IGCSE

INTRODUCTION

A time series consists of numerical data collected. observed or recorded at more or less regular intervals of time each hour, day, month, quarter or year. Examples of time series are the hourly temperature recorded, annual rain fall, etc.

SCATTER DIAGRAM

Scatter diagram is a graphic picture of the sample data. In scatter diagram different points are plotted. Due to fluctuations which includes seasonal, cyclical etc line is not drawn straight so we have to draw line of best fit.

TREND

A trend is a long term movement that persist for many years and indicates the general directions of the change of observed values.

GRAPH (LONG TERM CHANGE)

Source of image: https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhUwz937f6zWacwfDTzc1BMT3Od-PRIl8yaXernjsNwGjC0WeGAdI7RfYqOJ6NJIiuNBdBxVcxrQsbDdhOHim02UStTf_Wz9IjweG60EpwhXttWmQge6gOkvnLbE3npB_e6aPr1FHX_hByb/s400/long-term+trends.png

SEASONAL VARIATIONS

Variation which is caused by the change in seasons. Prices of different goods and services changes with the change in season. The main cause for seasonal variation are weather conditions, festival and customs.For example sale of ice cream are high in

the summer season, sale of sweaters are high in the winter season and low in the summer season. This represents seasonal fluctuation.

CYCLICAL VARIATIONS

These fluctuations occur around a long-term growth trend.There are two periods in the business cycle one is boom when economic activities and growth is high with increase demand for goods and services. This increases sales and business activity. Other period is recession when economic activity is down, prices decreases due to decrease demand for goods and services unemployment increases and economic activity slows down.

This shows economic cycle you can see fluctuation in the 2 periods.

ANALYZING THE TREND

Two Methods are used

1. Semi averages method
2. Moving averages method

THE METHOD OF SEMI AVERAGES

Divide the values in the series in the two equal parts. Find the averages of the values in each pa

rt and plot the average values against the midpoint of two parts. Then draw the straight line.

This straight line can be described by the mathematical equation

y=mx+c

m=gradient (RATE)

c=y intercept

x and y=constant

EXAMPLE

Year	Profit	Total	Averages
2005	10
2006	50	210	70
2007	150
2008	80
2009	120	300	100
2010	100

GRAPH

Finally we will draw the graph. First we will plot all the points given in the question, in this question year and profits were given so plot out the points you can see in blue and then join together. Next we will plot the two points (averages) we have calculated and join it together with a straight line (Not drawn in the below diagram). In this diagram it is represented by pink.

Ex: Now join these two pink points together making a straight line

Notes: If you have further query or need any additional resources please comment. Your suggestions will be highly appreciated.