Let the weight of the chickens be 
. Then 
where 
is the standard deviation of the weights and 
is the mean of the weights. Then, the statement you're given is 
.
Now, rewrite 
where 
. Then, look up 
in a standard normal table such that 
and then note 
. Solve for 
, and you are done.
Math is Fun
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Standard Deviation Formulas
To work out the mean, add up all the values then divide by how many. But hang on ... we are calculating the Sample Standard Deviation, so instead of dividing by how many (N), we will divide by N-1
Statistics - Calculating Mean given standard deviation and percentage. - Mathematics Stack Exchange
You have to use the fact that the weights are normally distributed. You're given the standard deviation, and a value for the left 4% of the distribution. You can calculate (or look up) how many standard deviations away from the mean you are at 4%. More on math.stackexchange.com
t test - How to calculate standard deviation when only mean of the data and sample size is available? - Cross Validated
Many a times it happens that you get comprehensive data at a group level and you have to compare one group against another but you don't have the data points separated. In these cases, how do we get standard deviation/standard error calculated from only the mean of the group and sample size? More on stats.stackexchange.com
What's the best way to calculate standard deviation in this problem? From October 20222
Calculating the standard deviation takes WAY too long with a calculator with a built-in function handy. The overall better way to answer questions regarding standard deviation is just to check with one has more spread. The term “standard deviation” just means on average how far all other non-mean numbers “deviate” from the mean. In this case, if you’re paying close attention, you’ll notice the frequency between the two tables are the same, it’s just the numbers are shifted to be higher on the right. This means that the standard deviation is the same, but the means are different More on reddit.com
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April 10, 2023ELI5: Standard deviation
The standard deviation basically gives you an idea of how far apart all the different measurements in a set are. When you have a set of numbers, the average (called the mean) equals all the numbers added up, then divided by the amount of numbers. The standard deviation tells describes the average distance of the measurements from the mean. The average distance to the average value. The bigger the difference, the larger the standard deviation. This tells you something about thing that you're measuring. Let's say you're tracking the scores of your classmates on the latest English exam. If the average (mean) is 6.7, and the standard deviation is 0.3, it means that your classmates, on average, scored pretty close to that grade. If the standard deviation is 2.9, it means that your classmates' scores were all over the place, some scoring very high, some scoring very low. Very simple example: take these 5 numbers: 3 9 7 4 2. Mean: 5 Std. deviation: 2.6 (rounded down). This means that the average 'distance' from the average (5) is 2.6 (either up or down). Edit: clarification More on reddit.com
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May 1, 2016How is standard deviation calculated?
Find the mean of the data set · Calculate the difference of each data point from the mean · Square each difference · Average these squares (this is the variance) · Take the square root of the variance
study.com
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Standard Deviation Equation, Formula & Examples - Lesson | Study.com
Why do we calculate standard deviation?
Standard deviation gives a good idea of the "shape" of a data set. It also holds several important properties for normal distributions, and it can be used to determine if a given data set is not normally distributed.
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Standard Deviation Equation, Formula & Examples - Lesson | Study.com
What is the formula to calculate standard deviation?
The formula for standard deviation is as follows: · {eq}\sigma = \sqrt{\sigma^2} = \sqrt{ \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2} {/eq}
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Standard Deviation Equation, Formula & Examples - Lesson | Study.com
Videos
Calculator.net
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Standard Deviation Calculator
A common estimator for σ is the sample standard deviation, typically denoted by s. It is worth noting that there exist many different equations for calculating sample standard deviation since, unlike sample mean, sample standard deviation does not have any single estimator that is unbiased, efficient, and has a maximum likelihood. The equation provided below is the "corrected sample standard deviation." It is a corrected version of the equation obtained from modifying the population standard deviation equation by using the sample size as the size of the population, which removes some of the bias in the equation.
Scribbr
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How to Calculate Standard Deviation (Guide) | Calculator & Examples
March 28, 2024 - We’ll use a small data set of 6 scores to walk through the steps. To find the mean, add up all the scores, then divide them by the number of scores. Subtract the mean from each score to get the deviations from the mean.
Cuemath
cuemath.com › data › standard-deviation
Standard Deviation - Formula | How to Calculate Standard Deviation?
In general, the standard deviation ... values: Find the mean, which is the arithmetic mean of the observations. Find the squared differences from the mean....
Study.com
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Standard Deviation Equation, Formula & Examples - Lesson | Study.com
June 30, 2013 - There is a specific series of steps that must be carried out in order: Find the mean of your data set. Subtract the mean from each of the data points. Take each of the differences and square them.
Top answer 1 of 3
3
Let the weight of the chickens be . Then where is the standard deviation of the weights and is the mean of the weights. Then, the statement you're given is .
Now, rewrite where . Then, look up in a standard normal table such that and then note . Solve for , and you are done.
2 of 3
0
You have to use the fact that the weights are normally distributed.
You're given the standard deviation, and a value for the left 4% of the distribution.
You can calculate (or look up) how many standard deviations away from the mean you are at 4%.
Given this, you multiply the number of standard deviations from the mean by the standard deviation (in lbs) to see how many lbs away from the mean you are.
You know one end (20 lbs) and you can now find the other end, which is the mean.
WHO
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Annex : Calculation of Mean and Standard Deviation
Now calculate the SD by taking the square root of the variance. ... The result is 2 mg/dL. Mean= ∑ x1 +x2 +x3+…. xn 3809 = 190.5 mg/dL ... Data points. ... The square root returns the result to the original units. The sum of the squared differences of each value from the mean (column C) is 71.
Indeed
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Calculating Standard Deviation: Example Included | Indeed.com Canada
April 24, 2025 - To simplify, you can round the answer to the nearest thousandth after finding the answer:√10 = 3.1622776601684This indicates that the example data set's average number is 10 and that each of the numbers in the data set deviates roughly 3.162 units apart from the average number. This makes sense when considering the data set of 6, 8, 12, and 14, because each of these values has a standard deviation of 3.162 units, meaning they're about 3.162 units away from the value of 10.Related: Analytical Skills: Essential for Every Job
Wikipedia
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Standard deviation - Wikipedia
8 hours ago - For each period, subtracting the expected return from the actual return results in the difference from the mean. Squaring the difference in each period and taking the average gives the overall variance of the return of the asset.
Investopedia
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Standard Deviation Formula and Uses, vs. Variance
June 5, 2025 - Standard deviation is a statistical measurement that looks at how far discrete points in a dataset are dispersed from the mean of that set. It is calculated as the square root of the variance.
YouTube
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How To Calculate The Standard Deviation - YouTube
This Statistics video tutorial explains how to calculate the standard deviation using 2 examples problems. You need to calculate the sample mean before you c...
Published September 26, 2019 Views 585K
CalculatorSoup
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Standard Deviation Calculator
November 4, 2025 - When working with data from a complete ... with a sample, divide by the size of the data set minus 1, n - 1. ... Take the square root of the population variance to get the standard deviation....
The BMJ
bmj.com › about-bmj › resources-readers › publications › statistics-square-one › 2-mean-and-standard-deviation
2. Mean and standard deviation
February 9, 2021 - The sum of the squares of the differences (or deviations) from the mean, 9.96, is now divided by the total number of observation minus one, to give the variance.Thus, ... from which we get This procedure illustrates the structure of the standard deviation, in particular that the two extreme ...
National Library of Medicine
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Standard Deviation - Finding and Using Health Statistics - NIH
Now divide by 9 (the total number of data points) and finally take the square root to reach the standard deviation of the data: This data shows that 68% of heights were 75 inches plus or minus 9.3 inches (1 standard deviation away from the mean), 95% of heights were 75’’ plus or minus ...
University of Southampton Library
library.soton.ac.uk › variance-standard-deviation-and-standard-error
Maths and Stats - Variance, Standard Deviation and Standard Error - LibGuides@Southampton at University of Southampton Library
November 10, 2025 - Standard deviation is the square root of the variance, and therefore is also a measure of spread - more specifically, it is a measure of dispersion (or, the measure of variability!). Where variance is used to show how much the values in a dataset vary from each other, the standard deviation exists to show how far apart the values in a dataset are from the mean, and therefore can be used to identify outliers.
Omni Calculator
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Standard Deviation of Sample Mean Calculator
January 18, 2024 - The formula to find the standard deviation of the sample mean is: ... We previously said that if we know the mean of the sampling distribution (μX̄), we also know the population mean (μ), as they're equal (μX̄ = μ). In practice, we never know μX̄, but we can estimate it using the sample mean (X̄). σX̄ indicates how X̄ approximates μ. The smaller σX̄, the nearest μ can be from our estimate.
Statistics LibreTexts
stats.libretexts.org › bookshelves › introductory statistics › introductory statistics (shafer and zhang) › 6: sampling distributions
6.1: The Mean and Standard Deviation of the Sample Mean - Statistics LibreTexts
March 27, 2023 - The mean \(\mu_{\bar{X}}\) and standard deviation \(σ_{\bar{X}}\) of the sample mean \(\bar{X}\) satisfy ... Equation \(\ref{average}\) says that if we could take every possible sample from the population and compute the corresponding sample mean, then those numbers would center at the number we wish to estimate, the population mean \(μ\).
Top answer 1 of 4
32
It's impossible. Consider any vector that has a mean of $0$ - multiply the values by $100$, and the standard deviation also increases by a factor of $100$, but the mean and sample size are unchanged. Both vectors have the same mean and $n$, but different SD. In general, you cannot find the standard deviation of the data given only the mean value and number of data points.
2 of 4
17
In general this is not possible, as noted in the other answers.
But, if you know (or assume) something about the underlying distribution from which the data points have been drawn, then it is sometimes possible.
The following table shows distributions where it is indeed relatively easy to do so. Shown are the parameters, mean $\mu$ and variance as given in the different Wikipedia links, as well as the standard deviation $\sigma = \sqrt{Var}$ with the mean substituted in and simplified.
| Distribution | Parameters | Mean $\mu$ | Variance | Standard Deviation |
|---|---|---|---|---|
| Poisson | $\lambda \ge 0$ | $\lambda$ | $\lambda$ | $\sqrt{\mu}$ |
| Exponential | $\lambda > 0$ | $1/\lambda$ | $1/\lambda^2$ | $\mu$ |
| Binomial | $n \in \mathbb{N}, 0 < p < 1$ | $np$ | $np(1-p)$ | $\sqrt{\mu - \mu^2/n}$ |
| (Central) chi-squared | $k \in \mathbb{N}$ | $k$ | $2k$ | $\sqrt{2\mu}$ |
| Maxwell-Boltzmann | $a>0$ | $2a\sqrt{2/\pi}$ | $\frac{a^2(3\pi-8)}{\pi}$ | $\mu\sqrt{\frac{3}{8}\pi-1}$ |
You may note that most of these distributions depend on only one parameter. I would conjecture that actually most single-parameter distributions for which closed-form solutions for both mean and variance exist allow you to deduce the standard deviation from the mean. So this table is probably incomplete.
Conversely, if the distribution depends on two parameters, it is quite unlikely that there is a simple relationship between mean and variance.
The following table shows some distributions where it is not possible to deduce the standard deviation just from the mean (and the sample size). Since many distributions fall into that category, this table is definitely not complete.
| Distribution | Parameters | Mean $\mu$ | Variance |
|---|---|---|---|
| Uniform | $a < b$ | $\frac{1}{2}(a+b)$ | $\frac{1}{12}(b-a)^2$ |
| Normal | $\mu, \sigma$ | $\mu$ | $\sigma^2$ |
| Student's-t | $\nu > 0$ | 0, for $\nu > 1$ | $\nu/(\nu-2)$, for $\nu > 2$ |
| Beta | $\alpha > 0, \beta > 0$ | $\alpha/(\alpha + \beta)$ | $\frac{\alpha\beta}{(\alpha+\beta)^2(\alpha+\beta+1)}$ |
| Gamma | $\alpha>0, \beta>0$ | $\alpha/\beta$ | $\alpha/\beta^2$ |
Note in particular the Student's t-distribution, which may be relevant due to the t-test tag on the question.