A company that supplies LP gas for heating keeps data on the low temperature for each day of the month. It summarizes these data by finding the mean, median, standard deviation, and interquartile range. The company assumes that people use the LP gas for heat when the temperature is below 70 degrees, so it creates a second set of data by subtracting 70 from each daily low temperature. Which of the four summary statistics will change for this second data set?

a. mean and median only
b. mean and standard deviation only
c. median and IOR only
d. standard deviation and IQR only
e. mean, median, standard deviation, and IQR

Step 1: An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean.

Step 2: The most common measure of variation, or spread, is the standard deviation. The standard deviation is a number that measures how far data values are from their mean.

Step 3: The standard deviation provides a numerical measure of the overall amount of variation in a data set, and can be used to determine whether a particular data value is close to or far from the mean

Step 4: Given the change in the values of all the data set, it implies that each of the values of mean, median, standard deviation and IQR is going to change.