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A CPI is a statistical estimate constructed using the prices of a sample of representative items whose prices are collected periodically. Sub-indices and sub-sub-indices can be computed for different categories and sub-categories of goods and services, which are combined to produce the overall index with weights reflecting their shares in the total of the consumer expenditures covered by the ...
However, from December 1982 through December 2011, the all-items CPI-E rose at an annual average rate of 3.1 percent, compared with increases of 2.9 percent for both the CPI-U and CPI-W. [28] This suggests that the elderly have been losing purchasing power at the rate of roughly 0.2 (=3.1–2.9) percentage points per year.
Mathematically, the variance of the sampling mean distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean.
This formula determines the overall inflation rate, which is the percentage change in the CPI over a given time period. In January 2024, the CPI increased 3.1 percent over the previous 12 months ...
The sample mean and sample covariance are not robust statistics, meaning that they are sensitive to outliers. As robustness is often a desired trait, particularly in real-world applications, robust alternatives may prove desirable, notably quantile-based statistics such as the sample median for location, [4] and interquartile range (IQR) for ...
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. [1] For example, the sample mean is a commonly used estimator of the population mean. There are point and interval ...
This shows that the sample mean and sample variance are independent. This can also be shown by Basu's theorem, and in fact this property characterizes the normal distribution – for no other distribution are the sample mean and sample variance independent. [3]
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.