It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
The estimate for the mean of a sample is denoted by ͞x, whereas the mean of the population is designated as μ. Further, parameters such as the mean,...

Precipitation and coprecipitation methods can be used to separate a mixture of ions in a solution. In qualitative inorganic analysis, ions that form sparingly soluble precipitates with the same reagent are separated based on the differences in solubility products. For example, consider the separation of Cu(II) and Fe(II) ions by precipitation as insoluble sulfides. First, copper(II) sulfide is precipitated by the addition of acidic H2S, where the dissociation of H2S is suppressed. Adding H2S...

The precipitation titration curve demonstrates the change in concentration of one reactant with the volume of titrant added. During the titration of chloride ions with silver nitrate, the precipitation titration curve is divided into three regions: before, at, and after the equivalence point. Before the equivalence point, low redissolution of the sparingly soluble silver chloride precipitate gives a low silver ion concentration. However, in the second region, representing the equivalence point,...

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...

The experimental conditions in a gravimetric analysis should be optimized to maximize the particle size and purity of the obtained precipitate. Ideally, the concentration of the precipitating reagent should be low with effective stirring to maintain low relative supersaturation for the growth of large crystals. In homogeneous precipitation, the precipitant is slowly generated by a chemical reaction in the solution to avoid local reagent excesses. For example, urea decomposes gradually to...

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:In the equation, x is an event, and P(x) is the probability of the event occurring.The expected value has practical applications in decision theory.This text is adapted from Openstax, Introductory Statistics, Section 4.2 Mean or Expected Value and...