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By Luyten W.J.

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Additional resources for Notes on Stellar Statistics III. On the Calculation of a Mean Absolute Magnitude from Apparent Magnitudes, Angular Proper Motions and Linear Radial Velocities

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For example, assume that the mean of 5 observations is fixed and it is 10. Then it is possible to select any set of 4 observations, as for example the set {8, 9, 10, 11}. However, given this set of values, the only way to obtain a mean of 10 is by having the fifth observation equal to 12 (similarly, if the set {2, 8, 10, 16} is chosen, the only way to obtain a mean of 10 is by selecting 14 as the fifth observation). We are not free to select the fifth value, therefore we say there are only 4 degrees of freedom.

Descriptive statistics 21 Measures of central tendency: mode, median, and mean The mode The mode is the most common value that occurs in a set of discrete data. 1) the mode was 26 since this was the score that occurred most often. If there are two most common values which occur with equal (or almost equal) frequency in a distribution of discrete data, then there are two modes, and the distribution is called bimodal. For example, imagine that a new type of cola drink is tasted by a sample of 30 people, and everyone rates how much they like it on a five-point scale (1 = not at all, 3 = neutral, 5 = very much).

Now the median  n  n + 1 corresponds to the value of either the   th or the   th ordered observation  2  2   n  n + 1 depending on n being even or odd. The   th, or the   th, ordered observation is 2    2  used to identify the interval within which the median is located. 2) the sample size is 40, so the median corresponds to the 20th ordered value. , between the 15th and the 29th ordered observations in the cumulative frequency distribution). The next step is to estimate the value of the 20th ordered observation.

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