Question

chapter 2: measures of center and spread
score: 1/10 answered: 1/10
question 2
which is more affected by extreme observations, the mean or median? and how about the standard deviation or iqr?
mean, standard deviation
mean, iqr
median, standard deviation
median, iqr

Explanation:

1. For measures of center: The mean is calculated as the sum of all values divided by the number of values. Extreme observations (outliers) can pull the mean in their direction. The median is the middle value when data is ordered, so it is resistant to extreme values (less affected by outliers).
2. For measures of spread: The standard deviation is calculated using the mean (since it involves deviations from the mean, \( \sigma=\sqrt{\frac{\sum (x_i - \mu)^2}{N}} \) for population, \( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n - 1}} \) for sample). Since the mean is affected by outliers, the standard deviation (which depends on the mean) is also affected by extreme values. The inter - quartile range (IQR) is \( IQR = Q_3 - Q_1 \), where \( Q_1 \) is the first quartile and \( Q_3 \) is the third quartile. Quartiles are based on the order of data, so IQR is resistant to extreme values (less affected by outliers).

So the mean is more affected by extreme observations than the median, and the standard deviation is more affected by extreme observations than the IQR.

Answer:

A. mean, standard deviation