Differentiating Standard Deviation and Standard Error

What is the primary purpose of error bars in data representation?

• To indicate the variability or precision of the data

• To compare different data sets

• To show the mean value of the data

• To highlight the highest and lowest values

What does a low standard deviation indicate about a data set?

• The data set has a high mean value

• The data set is not reliable

• The data set has a low degree of variability

• The data set has a high degree of variability

In the context of standard deviation, what does it mean if data points are scattered far from the mean?

• The data set has a low standard deviation

• The data set has a high standard deviation

• The data set is precise

• The data set is inaccurate

What does the standard error of the mean (SEM) quantify?

• The highest value in the data set

• The variability within a data set

• The precision of the mean

• The lowest value in the data set

How can you estimate the SEM using a single experiment?

• By dividing the mean by the sample size

• By multiplying the standard deviation by the sample size

• By dividing the standard deviation by the square root of the sample size

• By adding the standard deviation to the mean

What percentage of data points fall within plus or minus one standard deviation from the mean in a normal distribution?

• 50%

• 68%

• 95%

• 99%

What does it mean if SEM error bars do not overlap at all?

• The data sets are identical

• There is strong evidence that there is a difference between the two populations

• There is strong evidence that there is no difference between the two populations

• The data sets are unreliable

If SEM error bars overlap and the overlapping region includes the means of the sample, what can be concluded?

• The data sets are unreliable

• There is strong evidence that there is a difference between the two populations

• The data sets are identical

• There is strong evidence that there is no difference between the two populations

What happens to SEM error bars when you increase the number of samples in each population?

• They become smaller

• They become larger

• They disappear

• They remain the same

What is the relationship between the SEM value and the precision of the data?

• SEM value does not affect precision

• Lower SEM value means more precise data

• Higher SEM value means more precise data

• SEM value is unrelated to data precision