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| Math Central | Quandaries & Queries |
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A series of 100 measurements of a physical quantity have been made that show a random fluctuations characterized by a sample variance of 2% of the mean value. |
Please check your question! What you have above is unlikely, because variance and mean are dimensionally different. If the data are (eg) lengths, the mean will be a length and the variance will be a length squared.
If the series is lengthened to 1000 measurements made under the same
conditions, estimates the sample variance of the larger set of data.
The "sample variance" is the variance within the sample population. Under usual assumptions about the distribution (including the common assumption that the data are normally distributed with initially unknown mean and standard deviation), the best estimate for the bigger sample is that its variance and mean will be the same as those of the smaller sample.
RD
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Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.