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Sample and population variance

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Sample and population variance
Variance 256
Description
Exercise Name: Sample and population variance
Math Missions: High school statistics and probability Math Mission
Types of Problems: 2

The Sample and population variance exercise appears under the High school statistics and probability Math Mission. This exercise practices calculation of variance in both sample and population situations.

Types of Problems

There are two types of problems in this exercise:

  1. Find the mean and variance of the sample: This problem describes the measurements of a sample of all objects from a population. The student is asked to calculate the mean and the variance of the sample.
    Vars

    Find the mean and variance of the sample

  2. Find the mean and variance of the population: This problem describes the measurements of a population. The student is asked to calculate the mean and variance of the population.
    Varp

    Find the mean and variance of the population

Strategies

This exercise is medium to get accuracy badges because the calculation is intensive and the rounding restriction is subtle. Speed badges are medium but can be made easier with the calculator.

  1. The means are the same for both types of problems, but the sample variance is different than the population variance.
  2. The variance is the square of the standard deviation.
  3. For a population, the standard deviation is given by  {\sigma_x} , but for a sample it is  {S_x} .
  4. The TI83/84 calculators can find these standard deviations and then you can square them, but read carefully to be sure you are using the correct one.
  5. The problem asks answers to be rounded to the nearest tenth, so even if you have an exact decimal but it is to the hundredths, you need to round it to the tenths spot.
  6. The default cursor appears in the calculator app, so to start answering you need to click on the answer box.

Real-life Applications

  1. A population is a summation of all the organisms of the same group or species, which live in a particular geographical area. The population of humans can be calculated by adding the total number of people that live on the planet, although it is not always accurate.
  2. Dot plots, as most of statistics and a form of a graph, can be found in everyday media to display information to consumers.
  3. Data and statistics appear in news reports and in the media every day.
  4. Statistics can be seen more frequently than calculus in every day life.

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