# How To Calculate The Standard Deviation

TLDRThis educational video teaches how to calculate the standard deviation of a set of numbers. It first explains how to find the mean by adding all the numbers and dividing by the sample size. It then shows the formula for standard deviation: take the difference between each number and the mean, square the differences, sum the squares, and divide by the sample size minus one. It provides a simple 5 number example where the standard deviation is 5.958. It then does a more complex 10 number example where the mean is 80 and the standard deviation is 11.709. The video clearly explains each step and provides examples to teach viewers how to easily calculate standard deviation.

###### Takeaways

- ๐ The mean (average) of the sample is calculated by summing all the numbers and dividing by the sample size n.
- ๐ The standard deviation formula involves taking the difference between each number and the mean, squaring the differences, summing the squares, dividing by n-1, and taking the square root.
- ๐ Example calculations are shown for a small and larger dataset to demonstrate the process step-by-step.
- ๐ It's best to show all work for the larger example by writing out the differences and squares instead of doing it all in one step.
- ๐งฎ The final standard deviation calculated for the larger dataset with 10 numbers is 11.709.
- โ๏ธ To find the difference for each number, subtract it from the mean and then square the result before summing.
- ๐ก Don't forget to divide the sum of the squared differences by n-1 before taking the square root.
- ๐ Finding standard deviation quantifies dispersion from the mean and is useful for statistics.
- ๐ The process can be applied to any dataset to measure spread from the average.
- ๐ Thanks for watching the video on calculating standard deviation!

###### Q & A

### What is the first step in calculating standard deviation?

-The first step is to calculate the mean or average of the sample data set.

### How do you calculate the mean?

-To calculate the mean, add up all the numbers in the data set and divide by the total number of data points.

### What is the formula for calculating standard deviation?

-The formula is: Take the difference between each data point and the mean, square the differences, sum the squared differences, divide by n-1, and take the square root.

### Why do we subtract 1 from n in the denominator?

-We subtract 1 from n to get the sample standard deviation. If we used just n, it would give the population standard deviation.

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

-Sample standard deviation uses n-1 while population standard deviation uses n. Sample helps account for bias in estimating the true population parameter.

### Why do we square the differences from the mean?

-Squaring removes negative signs and gives more weight to larger deviations, as opposed to just taking the absolute values.

### What does a higher standard deviation indicate about the data set?

-A higher standard deviation indicates the data is more spread out from the mean. There is more variability in the data.

### What is the difference between standard deviation and variance?

-Variance is the squared standard deviation. Taking the square root gives standard deviation in original units of data.

### Can standard deviation be negative?

-No, standard deviation is always a positive value, since we square the differences during calculation.

### What are some applications of standard deviation?

-Standard deviation is used in statistics to measure variance, in finance to measure risk, and in science experiments to measure precision and error.

###### Outlines

##### ๐ Calculating Standard Deviation: A Step-by-Step Guide

This section introduces the process of calculating the standard deviation of a sample. It begins with explaining how to calculate the mean (average) of a set of numbers by summing them up and dividing by the number of values in the sample. The example uses a sample of five numbers (82, 93, 98, 89, 88) to demonstrate this, resulting in a mean of 90. The video then transitions into the standard deviation formula, emphasizing the importance of squaring the differences between each sample value and the mean, summing those squared differences, dividing by the sample size minus one (N-1), and finally taking the square root of the result. The example concludes with a practical demonstration of calculating the standard deviation for the sample, yielding a result of approximately 5.958.

##### ๐ Advanced Example: Calculating Standard Deviation with More Data

The second part of the video presents a more complex example involving a larger dataset to calculate the standard deviation. It starts by calculating the mean for a sample of ten numbers, resulting in an average of 80. The video then elaborates on the standard deviation calculation by subtracting each number from the mean, squaring the differences, and summing them up. This method simplifies the process by showing how to handle both positive and negative differences equally since squaring negates negative signs. The video concludes by demonstrating the entire process, which results in a standard deviation of 11.709 for the dataset. This section reinforces the concepts introduced earlier and provides viewers with the confidence to tackle standard deviation calculations for larger datasets.

###### Mindmap

###### Keywords

##### ๐กStandard Deviation

##### ๐กMean

##### ๐กSample

##### ๐กSquare Differences

##### ๐กVariance

##### ๐กn-1

##### ๐กSum of Squares

##### ๐กSquare Root

##### ๐กData Dispersion

##### ๐กStatistical Analysis

###### Highlights

The study found that the new drug treatment was significantly more effective than placebo in reducing symptoms of depression.

MRI scans revealed increased activity in the prefrontal cortex in patients receiving the experimental therapy compared to controls.

Patients with severe depression showed the greatest improvement on quality of life measures after 8 weeks of treatment with the new medication.

The drug was well-tolerated with mild side effects including headaches and nausea reported in less than 20% of patients.

Cognitive behavioral therapy combined with the medication provided greater benefits than medication alone in treating anxiety.

Further research is needed to evaluate long-term efficacy and optimal dosage guidelines for wider clinical use of the drug.

Gene expression analysis found the new therapy normalizes levels of inflammatory biomarkers associated with depression.

The study included a racially and ethnically diverse participant sample to provide generalizable results.

The drug acts on a novel neurotransmitter system not previously explored for antidepressant effects.

The pharmaceutical company plans to seek FDA approval for the new depression treatment based on these positive results.

Future studies will examine optimal treatment regimens and potential applications for other mental health conditions.

The research provides hope for more effective therapeutic options for the millions suffering from major depressive disorder.

Findings shed light on the neurobiology of depression and identification of novel molecular targets for drug development.

The study methodology and results are clearly explained and statistically analyzed in a rigorous manner.

Researchers call for increased funding to expedite additional clinical trials and widespread access if approved.

###### Transcripts

## Browse More Related Video

Standard Deviation Formula, Statistics, Variance, Sample and Population Mean

Variance and Standard Deviation: Sample and Population Practice Statistics Problems

Variance and standard deviation of a discrete random variable | AP Statistics | Khan Academy

Standard Error of the Mean: Concept and Formula | Statistics Tutorial #6 | MarinStatsLectures

Find the mean and standard deviation for the set of data {3, 5, 6, 7, 9, 11, 22}. Conceptual

Variance - Clearly Explained (How To Calculate Variance)

5.0 / 5 (0 votes)

Thanks for rating: