Measures of Central Tendency and Dispersion

The video tutorial explains the impact of outliers on data distribution, focusing on measures of central tendency like mean, median, and mode, as well as measures of dispersion such as variance and standard deviation. It demonstrates how an outlier can significantly alter the mean and standard deviation, while the median and mode remain unaffected. The tutorial concludes by recommending the use of median or mode over mean when outliers are present.

Which measure of central tendency is defined as the most frequently occurring value in a data set?

• Mean

• Standard Deviation

• Median

• Mode

What is the median of a data set?

• The spread of data around the mean

• The average value

• The middle value

• The most frequent value

What does the standard deviation measure in a data set?

• The middle value

• The average value

• The most frequent value

• The spread of data around the mean

Which of the following is a measure of dispersion?

• Variance

• Median

• Mean

• Mode

How is the mean of a data set calculated?

• By calculating the square root of variance

• By finding the middle value

• By adding all values and dividing by the number of values

• By identifying the most frequent value

What happens to the mean when an outlier is added to a data set?

• It becomes zero

• It increases

• It decreases

• It remains the same

What is the effect of an outlier on the standard deviation of a data set?

• It decreases

• It becomes zero

• It increases

• It remains the same

Which measure of central tendency is least affected by outliers?

• Mean

• Standard Deviation

• Median

• Mode

Why might we choose to use the median over the mean in the presence of outliers?

• The median is a measure of dispersion

• The median is always larger

• The median is not affected by outliers

• The median is easier to calculate

What is the primary reason for removing outliers from a data set?

• To increase the mean

• To prevent distortion of statistical measures

• To reduce the data set size

• To simplify calculations