# Solving Standard Deviation Homework Problem

• gtfitzpatrick
In summary: XZlIGlzIGVycm9yIHRoZSBwcm9wb3NhdGlvbiBtZWFuIGFuZCBzdGFuZGFyZCBkZXZpY2UgYW5kIHN0YW5kYXJkIGRldmljZS4gYSBuZXcgYmF0Y2ggY29tcGVzIHZvbHVtZSBpbiBhbmQgZ2l2ZSBhIGJhdGNoIGdhbWUgYSBtZWFuIHdoZXJlIHRoZSBvdmVyYWxsIGF2ZXJhZ

## Homework Statement

i'm given the population mean and standard deviation. A new batch comes in and given a random sample. the question asks do i believe the new batch has a different mean from the overall average?

## The Attempt at a Solution

so i got the mean and standard deviation of the new batch. They are much different from the population mean and standard deviation. But i don't believe they are different the sample standard deviation is less than the population standard deviation, am i right in my thinking?

You could make your "I think" more quantitative. For example, suppose that you are given the population mean and std.dev as $\mu$ and $\sigma$, and you measure a mean x on the random sample.

Now you can calculate the probability that if you were to do the experiment you just did, you would get a mean of at least x (or at most x, if $x < \mu$), assuming that $(\mu, \sigma)$ are the actual distribution.
If that gives you a very small probability (like 0.0002%) then that means that your assumption is probably incorrect - given that you've just done the experiment and still found that unprobable outcome.

gtfitzpatrick said:

## Homework Statement

i'm given the population mean and standard deviation. A new batch comes in and given a random sample. the question asks do i believe the new batch has a different mean from the overall average?

## The Attempt at a Solution

so i got the mean and standard deviation of the new batch. They are much different from the population mean and standard deviation. But i don't believe they are different the sample standard deviation is less than the population standard deviation, am i right in my thinking?

Was this last thing supposed to be a sentence in English? It isn't.

Google "t-test" and/or "F-test", although these require normally-distributed data.

RGV

## 1. What is standard deviation and why is it important in statistics?

Standard deviation is a measure of how spread out a set of data is from its mean. It is important in statistics because it helps us understand the variability and dispersion of a data set. It is also used to compare different data sets and make predictions based on the data.

## 2. How do you calculate standard deviation?

The formula for calculating standard deviation is as follows: Step 1: Calculate the mean of the data set by adding all the values and dividing by the total number of values.Step 2: Subtract the mean from each data point.Step 3: Square each difference.Step 4: Add all the squared differences together.Step 5: Divide the sum by the total number of values.Step 6: Take the square root of the quotient. This is the standard deviation.

## 3. What is the difference between population standard deviation and sample standard deviation?

Population standard deviation is calculated using the entire set of data, while sample standard deviation is calculated using a smaller subset of the data. Sample standard deviation is used when we only have a sample of the population, while population standard deviation is used when we have data for the entire population.

## 4. How do you interpret standard deviation?

The standard deviation can be interpreted as a measure of the spread of the data around the mean. A small standard deviation indicates that the data points are close to the mean, while a large standard deviation indicates that the data points are more spread out. It is also important to consider the context of the data and compare the standard deviation to the range of the data.

## 5. How is standard deviation used in real-world applications?

Standard deviation is used in a variety of real-world applications, such as quality control in manufacturing, risk assessment in finance, and analyzing trends in market data. It is also used in social sciences to measure the variability of survey responses and in natural sciences to analyze experimental data. Standard deviation is a valuable tool for understanding and making predictions based on data in many fields.