# Sample and population standard deviation

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Sample and population standard deviation
Description
Exercise Name: Sample and population standard deviation
Math Missions: High school statistics and probability Math Mission
Types of Problems: 2

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

## Types of Problems

There are two types of problems in this exercise:

1. Find the mean and standard deviation 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 standard deviation of the sample.
1. Find the mean and standard deviation of the population: This problem describes the measurements of a population. The student is asked to calculate the mean and standard deviation 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 standard deviation is different than the population standard deviation.
2. For a population, the standard deviation is given by ${\sigma_x}$, but for a sample it is ${S_x}$.
3. The TI83/84 calculators can find these standard deviations but make sure user is careful to use the correct one that the question is asking for.
4. The problem asks answers to be rounded to the nearest tenth, so even if user have an exact decimal but it is to the hundredths, they need to round it to the tenths spot.
5. The default cursor appears in the calculator app, so to start answering user needs to click on the answer box.

## Real-life Applications

1. Sport teams use standard deviation. For example, a team that may be consistently good may have low standard deviation, but a team that scores a lot standard deviation might be high.
2. Another scenario may be money. In money, standard deviation may mean the risk of the prices. If the investment loses money, it's going to have a low standard deviation.
3. Another scenario one might be considering the whether temperatures in two different areas. It helps people figure out which one has the highest deviation based on it variations.
4. Data and statistics appear in news reports and in the media every day.
5. Statistics can be seen more frequently than calculus in every day life.