Statistics Quiz

What does a larger standard deviation indicate about the data set compared to a smaller standard deviation?

• The data set has a higher mean.

• The data points are more spread out from the mean.

• The data points are closer to the mean.

• The data set is normally distributed.

According to the empirical rule, what percentage of data falls within one standard deviation of the mean in a normal distribution?

• 95%

• 75%

• 68%

• 50%

How does variability affect the interpretation of data in a statistical analysis?

• It indicates how consistent the data is.

• It has no effect on interpretation.

• It only affects the mean.

• It makes the data easier to analyze.

What are the key characteristics of a normal distribution?

• It has a bell-shaped curve and is symmetric around the mean.

• It is skewed to the left.

• It is always uniform.

• It has multiple peaks.

How do you calculate a z-score?

• (Data point - Mean) / Standard Deviation

• (Data point + Mean) / Standard Deviation

• (Mean - Data point) / Standard Deviation

• (Data point - Median) / Standard Deviation

What does the area under the curve of a normal distribution represent?

• The total number of data points.

• The mean of the data set.

• The standard deviation of the data set.

• The probability of a data point falling within a certain range.

If two data sets have the same mean but different standard deviations, how would their distributions differ?

• They would both be skewed.

• The one with the smaller standard deviation would be more spread out.

• The one with the larger standard deviation would be more spread out.

• They would be identical.

If a student has a z-score of +2, what does this indicate about their performance compared to their peers?

• They performed at the median.

• They performed below average.

• They performed above average, significantly better than most.

• They performed exactly at the average.

If the mean test score of a class is 75 with a standard deviation of 5, what range of scores would you expect approximately 68% of the students to fall within?

• 75 to 80

• 65 to 85

• 70 to 80

• 75 to 85

Can you provide an example of a real-life scenario where a normal distribution might be observed?

• The number of cars in a parking lot.

• The colors of marbles in a bag.

• Heights of adult humans.

• The number of students in a classroom.