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%

Tags

CCSS.HSS.ID.A.4

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

Tags

CCSS.7.SP.B.3

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

Tags

CCSS.7.SP.B.3

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