Question

christchurch, nz low temperatures (°c)
5 6 7 8 9 10 11 12 13 14 15
st. louis, mo low temperatures (°c)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
chicago, il low temperatures (°c)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
london, uk low temperatures (°c)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
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 cooler each day. the two cities have the same variability in temperature and so they have the same standard deviation.
3 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 doesn't imply zero standard deviation.

Step2: Analyze St. Louis and Chicago data

Adding or subtracting a constant to each data - point (like 3 degrees cooler in Chicago than St. Louis) doesn't change the spread (variability), so standard deviations are equal.

Step3: Compare Chicago and London data

London has the same high temperatures as Chicago except on the last day, and its last - day temperature is more extreme, increasing the variability and thus the standard deviation.

Answer:

1. False. The standard deviation is a measure of variability and there is some variability in the data set.
2. True. Chicago's temperatures are the same as St. Louis's, but 3 degrees cooler each day. The two cities have the same variability in temperature and so they have the same standard deviation.
3. True. London has the same high temperatures as Chicago except on the last day. London's temperature is more extreme on the last day. Therefore, the temperatures in London have more variability than Chicago's temperatures on these days.