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.
2. the standard deviation of st. louiss temperatures is equal to the standard deviation of chicagos temperatures.
3. the standard deviation of chicagos temperatures is less than the standard deviation of londons temperatures.

Explanation:

Step1: Recall standard - deviation concept

Standard deviation measures variability. Symmetry of data does not mean standard deviation is zero. There is variability in Christchurch's data, so the statement about Christchurch is false.

Step2: Analyze St. Louis and Chicago data

If Chicago's temperatures are the same as St. Louis's but 2 degrees colder each day, the spread (variability) of the data is the same. Since standard deviation measures variability, their standard - deviations are equal.

Step3: Compare Chicago and London data

If London has the same temperatures as Chicago except on the last day and London's temperature is higher on the last day, London's data has more variability than Chicago's. So, the standard deviation of Chicago's temperatures is less than that of London's.

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 2 degrees colder 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 temperatures as Chicago except on the last day. London's temperature is higher degrees warmer than Chicago's. Therefore, the temperatures in London have more variability than Chicago's temperatures on these days.