Estimate standard deviation of sample

Question

You have a random sample of 25 objects with mean weight of 24 grams, estimate the standard deviation of the sample.

In addition, you know it's supposed to be 25 grams with a deviation of 1 gram, but this has no relevance to the above question, right?

How is this done? Looking in my formula reference this is not enough information to give an estimate.

Answer 1

Standard deviation is $0$ because all the samples are completely random.

Answer 2

A sample mean of $24$ is unlikely from a sample of twenty-five items with a population mean of $25$ and population standard deviation of $1$. So the sample casts doubt on the population parameters.

But conditioned on the data given and ignoring issues such as finite populations, a good estimate of the variance of the sample conditioned on the population mean and sample mean is the same as the population mean. $1$ in this case.

Here is an illustration of ten thousands trials in R from a normal distribution, suggesting no relationship between the sample standard deviation and the difference between the population mean and the sample mean

library(matrixStats)
samplesize <- 25
cases      <- 10000
popmean    <- 25
popsd      <- 1
set.seed(1)
matdat <- matrix(rnorm(ss*cases, mean=popmean, sd=popsd), ncol=ss)
samplemeans <- rowMeans(matdat)
samplesds <- rowSds(matdat)
plot(samplesds ~ samplemeans)