Exploring Standard Deviation in Data Sets

What is the main purpose of statistics as discussed in the lesson?

• To calculate probabilities

• To measure the central tendency of data

• To answer questions involving variability

• To create visual data representations

Which of the following is NOT part of the five-number summary?

• Minimum

• Median

• Mean

• Third Quartile

What does the interquartile range (IQR) represent?

• The difference between the maximum and minimum values

• The range of the middle 50% of the data

• The average value of the data set

• The sum of all data points

How is the IQR calculated?

• Sum of all data points divided by the number of data points

• Mean minus Median

• Third Quartile minus First Quartile

• Maximum minus Minimum

What does a larger IQR indicate about a data set?

• More data points

• Smaller range

• Greater variability

• Greater central tendency

What is the standard deviation used to measure?

• The spread of the middle 50% of the data

• The total sum of all data points

• The central value of a data set

• The average distance of data points from the mean

Which symbol typically represents the sample standard deviation in a calculator?

• σ

• μ

• s

• x̄

How does the standard deviation of a data set compare to the IQR?

• It is usually twice the IQR

• It is always equal to the IQR

• It is unrelated to the IQR

• It is often close to half the IQR

What does it mean if a data point is within one standard deviation of the mean?

• It is an outlier

• It is within the middle 50% of the data

• It is the median

• It is closer than one standard deviation to the mean

What percentage of data typically falls within one standard deviation of the mean?

• Less than 50%

• Exactly 75%

• Exactly 50%

• More than 50%