# Introduction & Descriptive Statistics Essay

INTRODUCTION & DESCRIPTIVE STATISTICS

BASIC CONCEPTS

Situation: A journalist is preparing a program segment on what appears to be the relatively disadvantaged financial position of women and the incidence of female poverty in Australia.

Several questions may arise, for example: • What is the pattern of female incomes? • How severe is the problem of female poverty and what proportion fall below the ‘poverty line’? • Has their general level of income improved over the last ten years? • Are single working mothers especially disadvantaged? • Working mothers often need to put their children into day-care. What should the capacity of the local centre be? • How does their income compare with their

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We are interested in describing this overall behaviour. Some features of particular interest are

• Dominant values that tend to occur more often than the others

These are called Modes. There can be one or more modes.

Eg.

• Measures of Location: Single values that can be used to represent the whole group of cases

The Median is the value that has half the cases below it.

Eg.

The Mean is the simple average of all the values.

Eg.

• The Amount of Variation

The Observed Variety of Values

Eg.

The Range is the difference between the highest and lowest value

Eg.

The Standard Deviation is the square root of the average squared difference between the mean and each of the cases

Eg.

The Variance is the average squared difference between the mean and each of the cases

Eg.

• The Type of Variation

Skewness is a tendencies towards the higher or the lower values. It is positive when the pattern leans to the left and negative when it leans to the right. There is no skewness if the pattern is symmetrical.

Eg.

Kurtosis is a tendencies towards or away from the dominant or representative values. It is mesokurtic when the cases tend to be drawn