Properties of Mean, Median and Mode PDF

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Properties of Mean, Median and Mode Properties of Mean, Median and Mode Properties of Mean 1. Mean can be calculated for any set of numerical data. 2. A set of numerical data has one and only one mean. 3. Mean is the most reliable measure of central tendency since it takes into account every item in the set of data. 4. The mean is affected by unusually large or small data values. 5. The sum of the differences between individual observations and the mean is zero. 6. The product of the mean and the number of items on which mean is based is equal to the sum of all given items.

2. It is not affected by extremely large or small values and is therefore a valuable measure of central tendency when such values occur. 3. It is not applicable to qualitative data. 4. Median is used when the data are ordinal. 5. Median can determine by graphic method. 6. The sum of the absolute deviations taken from the median is less than the sum of the absolute deviations taken from any other observation in the data. When to use the median? The median is used when either one of two conditions are met. If the,

7. The sum of squares of deviation of set of values about its mean is minimum.

1. Data is ordinal 2. Distribution is skewed or non-normal.

8. If each item of the original series is replaced by the actual mean, then the sum of those substitutions will be equal to the sum of the individual items.

Properties of Mode

9. Mean is not independent of change of origin and change of scale.

1. The mode is the easiest to compute. 2. The mode is not always unique. A data set can have more than on mode, or the mode may not exist for a data set.

When to use the mean?

3. Can be used for qualitative as well as quantitative data.

The mean is used when both of the following conditions are met:

4. Not affected by extreme values.

1. Data is scaled a) Data with equal intervals like speed, weight, height, temperature, etc. 2. Distribution is normal b) The mean is sensitive to outliers that are found in skewed distributions, you should only use the mean when the distribution is more or less normal. Properties of Median 1. There is a unique median for each data set.

5. The mode can be used when the data are nominal or categorical, such as religious preference, gender, or political affiliation. 6. It cannot be manipulated algebraically: modes of subgroups cannot be combined. When to use the mode? The Mode is used when you want to know the most frequent response, number or observation in a distribution....