Which measure of central tendency is most affected by extreme values of the distribution?

1. Geometric mean
2. Arithmetic mean
3. Median
4. Mode

Answer (Detailed Solution Below)

Option 2 : Arithmetic mean

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HP JBT TET 2021 Official Paper

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Measures of central tendency provides a single value that indicates the general magnitude of the data and this single value provides information about the characteristics of the data by identifying the value at or near the central location of the data.

• Mean or Arithmetic mean for sample is denoted by symbol ‘M or x̅ (‘x-bar’)’ and mean for population is denoted by ‘µ’ (mu). It is one of the most commonly used measures of central tendency and is often referred to as average.
• It can also be termed as one of the most sensitive measure of central tendency as all the scores in a data are taken in to consideration when it is computed.

Properties of Mean:- 

• Mean is sensitive to the actual position of each and every score in a distribution and if another score is included in the distribution, then the mean or average of that distribution will change. 
• It is affected most by extreme scores as it includes all the data in a series.
• Mean is especially effective when we want the measure of central tendency to reflect the sum of the scores.

Thus, it is concluded that Arithmetic mean is most affected  by extreme scores.

• Median is a point in any distribution below and above which lie half of the scores. The middle score in this distribution is then identified as median.
• Mode is denoted by symbol ‘Mo’. Mode is the score in a distribution that occurs most frequently.
• Geometric mean is an average based on the product of items. When the number of, items is three or more, finding their product and extracting its roots becomes difficult.

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Measures of central tendency are numbers that indicate the centre of a set of ordered numerical data.

The three common measures of central tendency are the mean, the median and the mode.

The mean gives each element of a data set equal weight. When there are no extreme numbers in the data set (no very low or very high numbers), the mean is a good choice for a measure of central tendency. Statisticians state that "the mean is the most unbiased measure of central tendency".

The median gives the greatest weight to elements in the middle of the ordered data. When there are extreme numbers in the data set (very low or very high numbers), the median is a good choice for a measure of central tendency. The extreme numbers have less effect (or no effect at all) on the median.

The mode is a good choice for a measure of central tendency when the data has many identical data values.

The data below are the hourly sales of songs for an on-line music store over a ten hour period.

RAW DATA: { 11, 10, 13, 15, 73, 69, 67, 66, 14, 12 }

ORDERED DATA: { 10, 11, 12, 13, 14, 15, 66, 67, 69, 73 }

Mean: 35

Median: 14.5

Mode: There is no mode.

Given the way the data is distributed in this example (with many small and many large numbers), the arithmetic mean is probably the most appropriate measure of central tendency.

The mean number of songs sold at an on-line music store over a ten hour period is 35. [Open a demonstration(with the data of this example pre-entered).]

The data below are the yearly wages (in dollars) of ten people working at an on-line music store.

DATA: { 41 000, 41 000, 41 000, 41 000, 43 000, 45 000, 48 000, 50 000, 50 000, 250 000 }

Mean: 65 000

Median: 44 000

Mode: 41 000

Given the way the data is distributed in this example (with one persons yearly wage being so large), the median is probably the best measure of central tendency.

NOTE: Nine people are below the mean and one person is above the mean, so the mean is probably not the most appropriate measure of central tendency.

NOTE: The majority of people working at the store (four in this case) are new employees who earn "starting wages". The mode, therefore, is probably not the most appropriate measure of central tendency.

The median yearly wage of ten people working at an on-line music store is $44 000.00. [Open a demonstration (with the data of this example pre-entered).]

The data below are the seventeen shoe sizes of one type of shoe sold in one day at a local shoe store.

DATA: { 5, 6, 7, 7, 7, 7, 7, 7, 8, 9, 9, 10, 11, 12, 13, 13, 15 }

Mean: 9

Median: 8

Mode: 7

Given the way the data is distributed in this example (with so many size seven shoes being sold), the mode is probably the best measure of central tendency.

The mode shoe size of one type of shoe sold at a local shoe store is size seven. [Open a demonstration (with the data of this example pre-entered).]

Which measure of central tendency is most affected by an extreme value?

What measures most affected by extreme values?

Which measure of central tendency is affected by extreme observations?