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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

User M Murteza
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1 Answer

4 votes

Final answer:

The summary statistics that will change for the second data set, where 70 is subtracted from each temperature, are mean and median only, since these depend on the location of the data, not its spread.

Step-by-step explanation:

When a company that supplies LP gas subtracts a constant value of 70 from each daily low temperature to track usage, the four summary statistics mentioned—mean, median, standard deviation, and interquartile range—will be affected differently. Subtracting 70 from each temperature will shift the data set down by 70 units without altering the spread or shape of the data distribution.

The mean will decrease by 70 because the mean is sensitive to every single data point. The median will also decrease by 70 because it is the middle value of the ordered data, and shifting all data by the same amount will shift the median too. The standard deviation will not change because standard deviation is a measure of spread about the mean, not its location. Since all values are equally adjusted, the spread remains the same. The interquartile range (IQR) will also remain unchanged for a similar reason; it is determined by the difference between the third and first quartiles (Q3-Q1), and since both are shifted by the same amount, the range between them is unaffected.

Therefore, the appropriate answer to the original question is that the summary statistics that will change for the second data set are mean and median only.

User Feng Smith
by
5.1k points
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