3. Describing Data Numerically

Suppose you have a random sample of size $n$ from a population with standard deviation $\sigma$. To calculate the standard error of the sample mean, which formula should you use, and under what condition can you assume the sampling distribution of the mean is approximately normal?

Is the $standarddeviation$ considered a resistant measure of spread in statistics?

Which of the following is not a property of the $standarddeviation$?

As the mean $\mu$ increases in a normal distribution, what happens to the graph of the normal curve?

A sample of $n=4$ scores has ${\mathrm{SS}}_S=60$. What is the variance for this sample?

Which of the following statements about the shape of a normally distributed data set is true?

If the variance of a data set is $3.6$ grams squared, what is the standard deviation in grams?

Suppose you have two histograms, Histogram A and Histogram B, each representing the distribution of exam scores for two different classes. Histogram A shows scores tightly clustered around the mean ($\mu$), while Histogram B shows scores spread out over a wider range. Based on this information, which histogram depicts a higher standard deviation ($\sigma$)?

Which of the following characteristics does not describe a normal distribution?

What is the standard deviation of the following sample data: $2$, $6$, $2$, $0$, $5$?

A sample of $n=4$ scores has $SS=60$. What is the variance for this sample?

Given the data set $0.40$, $0.72$, $1.15$, $2.14$, what is the variance of the data set? Round your answer to the nearest hundredth.

Given four histograms representing different data sets, each with the same mean $\mu$ but varying spreads, which histogram would correspond to the largest standard deviation $\sigma$?

Which of the following values can the variance of a dataset never be?

Suppose you have two histograms, A and B, each representing the distribution of exam scores for two different classes. Histogram $A$ shows scores tightly clustered around the mean, while Histogram $B$ shows scores spread out over a wider range. Which histogram depicts a higher $\mathrm{standard} \mathrm{deviation}$?