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Central Tendency

What are Measures of Central Tendency?

Measures of central tendency are statistical methods used to determine the "center" of a set of data. The three most common measures of central tendency are: the mean, the median, and the mode. Each measure of central tendency has its own advantages and disadvantages, and we should choose the most appropriate one based on different types of data and situations.

The Mean

The mean, or the arithmetic average of a set of observations, is equal to the sum of the measurements divided by the number of observations.

The Mode

The mode of a set of numbers is the most commonly occurring value.

The Median

The median of a set of numbers is the middle number (or the average of the two middle values) when the observations are arranged in ascending order. Therefore, half of the observations are higher than the median, and half of the observations lie below the median.

The Skewness

Skewness is a measure of the asymmetry in observations due to extreme values. If there are more extreme large values than small values, the data is skewed to the right. On the other hand, if there are more extreme small values than large values, then the data is skewed to the left.

Example - Death Valley Daily High Temperatures, July 2013

  • July 1 - 127
  • July 2 - 127
  • July 3 - 128
  • July 4 - 126
  • July 5 - 125
  • July 6 - 121
  • July 7 - 122
  • July 8 - 122
  • July 9 - 123
  • July 10 - 120
  • July 11 - 103
  • July 12 - 115
  • July 13 - 108
  • July 14 - 120
  • July 15 - 121
  • July 16 - 115
  • July 17 - 116
  • July 18 - 120
  • July 19 - 124
  • July 20 - 122
  • July 21 - 115
  • July 22 - 114
  • July 23 - 108
  • July 24 - 118
  • July 25 - 122
  • July 26 - 121
  • July 27 - 102
  • July 28 - 110
  • July 29 - 127
  • July 30 - 127
  • July 31 - 127


Mean: 118 | Median: 120 | Mode: 122

Why Investors Should Care About Measures of Central Tendency

Limiting Loss

The wider the swings in an investment's price, the greater chance of a loss on investment.

Uncertainty

In certain types of investments, such as a retirement savings account, investors want to have as little uncertainty as possible.

Opportunity

Price volatility presents arbitrary opportunities to buy assets cheaply and then sell them when they are overpriced.

Value

Using volatility helps investors calculate the right value for an investment, especially for investments with a complicated structure.