Decile

Decile

What is a decile?

A decile is a quantitative method of splitting a set of data classified into 10 equally important subsections. This type of data classification is carried out in the context of numerous university and statistical studies in the fields of finance and economics. Data can be ranked from largest to lowest value, or vice versa.

A decile, which has ten categorical compartments, can be contrasted with percentiles that have one hundred, quartiles that have four, or quintiles that have five.

Understanding the deciles

In descriptive statistics, a decile is used to rank large data sets from the highest values ​​to the lowest values, or vice versa. Like the quartile and the percentile, a decile is a form of quantile that divides a set of observations into samples that are easier to analyze and measure.

While quartiles are three data points that divide an observation into four equal groups or quarters, a decile consists of nine data points that divide a set of data into ten equal parts. When an analyst or statistician classifies the data and then divides it into deciles, it does so in order to discover the largest and smallest values ​​by a given metric. For example, by dividing the entire S&P 500 Index into deciles (50 companies in each decile) using the P / E multiple, the analyst will discover the companies with the highest P / E ratings and the lower in the index.

A decile is generally used to assign decile ranks to a dataset. A decile ranks the data in order from lowest to highest and is done on a scale of one to ten where each successive number corresponds to an increase of 10 percentage points. In other words, there are nine decile points. The 1st decile, or D1, is the point that has 10% of the observations below, D2 has 20% of the observations below, D3 has 30% of the observations below, and so on.

There is not a single way to calculate a decile; however, it is important that you are consistent with the formula you decide to use to calculate a decile. A simple calculation of a decile is:

The

D1=Value [[[[not+110]data begin {aligned} & text {D1} = text {Value of} left [ frac{ n + 1 }{ 10 } right ] text {th Data} \ end {aligned}

TheD1=Value [[[[10not+1The]dataTheThe

The

D2=Value [[[[2×(not+1)10]data begin {aligned} & text {D2} = text {Value of} left [ frac{ 2 times ( n + 1 ) }{ 10 } right ] text {th Data} \ end {aligned}

TheD2=Value [[[[102×(not+1)The]dataTheThe

The

D3=Value [[[[3×(not+1)10]data begin {aligned} & text {D3} = text {Value of} left [ frac{ 3 times ( n + 1 ) }{ 10 } right ] text {th Data} \ end {aligned}

TheD3=Value [[[[103×(not+1)The]dataTheThe

The

D9=Value [[[[9×(not+1)10]data begin {aligned} & text {D9} = text {Value of} left [ frac{ 9 times ( n + 1 ) }{ 10 } right ] text {th Data} \ end {aligned}

TheD9=Value [[[[109×(not+1)The]dataTheThe

From this formula, it is given that the 5th decile is the median since 5 (n + 1) / 10 is the data point which represents the halfway point of the distribution.

Key points to remember

  • A decile is a quantitative method of splitting a set of data classified into 10 equally important subsections.
  • A decile ranks the data in order from lowest to highest and is done on a scale of one to ten where each successive number corresponds to an increase of 10 percentage points.
  • This type of data classification is carried out in the context of numerous university and statistical studies in the fields of finance and economics.

Deciles in finance and economics

Deciles are used in the investment area to assess the performance of a portfolio or group of mutual funds. The decile rank acts as a comparative number that measures the performance of an asset compared to similar assets.

For example, suppose an analyst assesses the performance of a set of mutual funds over time, a mutual fund ranked 5 on a decile scale of 1 to 10 means that it is in the top 50%. By dividing mutual funds into deciles, the analyst can examine the best and worst performing mutual funds for a given period, ranked from lowest to highest average return on investment.

The government also uses deciles to determine the level of income inequality in the country, that is, how income is distributed. For example, if the top 20 workers in a country of 50,000 citizens fall into the 10th decile and earn more than 50% of the country’s total income, it can be concluded that there is a very high degree of income inequality in this country . In this case, the government can introduce measures to reduce the wage gap, such as increasing the income tax of the wealthy and creating property taxes to limit the amount of wealth that can be passed on to beneficiaries by heritage.

Example of deciles

The table below shows the non-grouped scores (out of 100) for 30 exam candidates:

48

52

55

57

58

60

61

64

65

66

69

72

73

75

76

78

81

82

84

87

88

90

91

92

93

94

95

96

97

99

Using the information presented in the table, the 1st decile can be calculated as:

  • = Value of [(30 + 1) / 10]data
  • = Value of 3.1st given, which is 0.1st of the path between scores 55 and 57
  • = 55 + 2 (0.1) = 55.2 = D1
  • D1 means that 10% of the data set falls below 55.2.

Let’s calculate the 3rd decile:

  • D3 = value of 3 (30 + 1) / 10
  • D3 = Value of 9.3th position, which is 0.3 between the scores of 65% and 66%
  • So, D3 = 65 + 1 (0.3) = 65.3
  • 30% of the thirty observation scores are less than 65.3%.

What would we get if we calculated the 5th decile?

  • D5 = value of 5 (30 + 1) / 10
  • D5 = value of the 15th position, halfway between scores 76 and 78
  • D5 is 77.

Also note that the 5th decile is also the median of the observation. Looking at the data set in the table, the median, which is the central data point for any given set of numbers, can be calculated as (76 + 78) / 2 = 77 = median = D5. At this point, half of the scores are above and below the distribution.

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