Question

decide if each statement is true or false. explain your reasoning

1. the standard deviation of christchurchs temperatures is zero because the data is symmetric

false the standard deviation is a measure of variability and there is some variability in the data set

1. the standard deviation of st. louiss temperatures is equal to the standard deviation of chicagos temperatures

true chicagos temperatures are the same as st. louiss, but 3 degrees colder each day. the two cities have the same variability in temperature and so they have the same standard deviation

1. the standard deviation of chicagos temperatures is less than the standard deviation of londons temperatures

true london has the same high temperatures as chicago except on the last day, londons temperature is degrees warmer than chicagos. therefore, the temperatures in london have more variability than chicagos temperatures on these days

Explanation:

Step1: Understand standard - deviation concept

Standard deviation measures data variability. Symmetry does not imply zero standard - deviation.

Step2: Analyze St. Louis and Chicago data

If two data - sets have the same shape (just shifted), they have the same variability and thus the same standard deviation. Chicago's data is just a shifted version of St. Louis's data.

Step3: Compare Chicago and London data

London has similar high - value patterns as Chicago, but with an outlier (last day), increasing its variability compared to Chicago.

Answer:

1. False
2. True
3. True