Comparing Data and Standard Deviation

How can you compare the centers of two data sets?

• By using the range of the data sets

• By calculating the standard deviation

• By using measures such as the mean or median

• By counting the number of data points

What is the definition of standard deviation?

• A measure of the average of a set of values.

• A measure of the amount of variation or dispersion in a set of values.

• A measure of the central tendency of a data set.

• A measure of the maximum value in a data set.

How can you determine if a data set is skewed?

• A data set is skewed if the mean and median are equal.

• A data set is positively skewed if the mean is less than the median.

• A data set is negatively skewed if the mean is greater than the median.

• A data set is considered skewed if the mean and median are not equal.

What is the median (Q2) in a data set?

• The median is the highest value in a data set.

• The median is the average of all values in a data set.

• The median is the middle value of a data set when ordered from least to greatest.

• The median is the sum of all values in a data set divided by the number of values.

How can outliers affect the mean and standard deviation?

• Outliers have no effect on the mean or standard deviation.

• Outliers can significantly affect the mean by pulling it towards their value, leading to a misleading representation of the data's central tendency.

• Outliers only affect the median, not the mean or standard deviation.

• Outliers decrease the standard deviation, indicating less variability.

How does standard deviation relate to the mean of a data set?

• Standard deviation measures the average of the data points.

• Standard deviation quantifies how much the values in a data set deviate from the mean.

• Standard deviation is the same as the mean of the data set.

• Standard deviation indicates the maximum value in the data set.

What does it mean for data to be normally distributed?

• Data is normally distributed when it follows a bell-shaped curve, where most of the observations cluster around the central peak (mean) and probabilities for values further away from the mean taper off equally in both directions.

• Data is normally distributed when all values are equally likely to occur, resulting in a uniform distribution.

• Data is normally distributed when it has a positive skew, meaning that the tail on the right side is longer or fatter than the left side.

• Data is normally distributed when it contains outliers that significantly affect the mean and standard deviation.

What does it mean if one data set has a higher median than another?

• It indicates that the central value of that data set is greater, suggesting that, on average, the values in that data set are higher.

• It means that the data set has more outliers than the other.

• It shows that the data set is more spread out than the other.

• It implies that the data set has a lower range than the other.

What is the purpose of calculating the mean in a data set?

• To provide a measure of central tendency, giving an average value that summarizes the data set.

• To identify the maximum value in the data set.

• To determine the range of the data set.

• To calculate the median value of the data set.

What is the significance of the interquartile range (IQR) in data analysis?

• It measures the average of the data set.

• It measures the spread of the middle 50% of a data set.

• It identifies the mode of the data set.

• It calculates the total range of the data set.