Question

meteorologist preparing a talk about global warming compiled a list of weekly low temperatures (in degrees Fahrenheit) he observed at his southern Florida home last year. The coldest temperature for any week was 36°F, but he inadvertently recorded the Celsius value of 2°. Assuming that he cor- rectly listed all the other temperatures, explain how this error will affect these summary statistics:

Answer 1

Regarding Measures of center, the Mean will be smaller, and Median will not be affected. Thus, the median will not change, since the temperature was already low initially and only decreased. However, the median takes the average of all values into account, and if you substitute a value for a smaller value, the average decreases.

In relation to Measures of spread, the range and standard deviation will be larger, and the IQR will not change. Therefore, the range is the highest minus the lowest number; if the lowest number decreases sharply, the range increases. On the other hand, the IQR only counts the first and third quartile values. Therefore, since the value was already the lowest, if it is decreased, it will not change the IQR. However, the standard deviation will increase significantly, as the decreasing value of the lowest data point will increase the overall spread.

Step-by-step explanation: