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03 Aug 2026, 07:52
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Cedar Court and Maple Court have the same number of apartments. Was the average (arithmetic mean) monthly electricity usage per apartment in Cedar Court greater than the average (arithmetic mean) monthly electricity usage per apartment in Maple Court?
(1) The median monthly electricity usage per apartment in Cedar Court was greater than the median monthly electricity usage per apartment in Maple Court.
(2) The range of the monthly electricity usage per apartment in Cedar Court was the same as the range of the monthly electricity usage per apartment in Maple Court.
(1) The median monthly electricity usage per apartment in Cedar Court was greater than the median monthly electricity usage per apartment in Maple Court.
(2) The range of the monthly electricity usage per apartment in Cedar Court was the same as the range of the monthly electricity usage per apartment in Maple Court.
03 Aug 2026, 07:52
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Official Solution:
Cedar Court and Maple Court have the same number of apartments. Was the average (arithmetic mean) monthly electricity usage per apartment in Cedar Court greater than the average (arithmetic mean) monthly electricity usage per apartment in Maple Court?
We need to determine whether the average for Cedar Court was greater than the average for Maple Court. Since both had the same number of apartments, this is equivalent to determining whether the total usage for Cedar Court was greater than the total usage for Maple Court.
(1) The median monthly electricity usage per apartment in Cedar Court was greater than the median monthly electricity usage per apartment in Maple Court.
A greater median does not guarantee a greater average. One building could have a higher median but a lower average if the data are distributed differently. Not sufficient.
(2) The range of the monthly electricity usage per apartment in Cedar Court was the same as the range of the monthly electricity usage per apartment in Maple Court.
Having the same range also does not determine the average. Two groups can have the same range but different averages. Not sufficient.
(1)+(2) Even together, a greater median and the same range still do not determine which building had the greater average.
Example 1:
• Cedar Court: 4, 5, 6
• Maple Court: 1, 2, 3
Here, Cedar Court has the greater median, and the two groups have the same range. The total usage for Cedar Court is greater than the total usage for Maple Court.
Example 2:
• Cedar Court: 1, 4, 5
• Maple Court: 2, 3, 6
Here, Cedar Court has the greater median, and the two groups have the same range. The total usage for Cedar Court is less than the total usage for Maple Court.
Not sufficient.
Answer: E
Cedar Court and Maple Court have the same number of apartments. Was the average (arithmetic mean) monthly electricity usage per apartment in Cedar Court greater than the average (arithmetic mean) monthly electricity usage per apartment in Maple Court?
We need to determine whether the average for Cedar Court was greater than the average for Maple Court. Since both had the same number of apartments, this is equivalent to determining whether the total usage for Cedar Court was greater than the total usage for Maple Court.
(1) The median monthly electricity usage per apartment in Cedar Court was greater than the median monthly electricity usage per apartment in Maple Court.
A greater median does not guarantee a greater average. One building could have a higher median but a lower average if the data are distributed differently. Not sufficient.
(2) The range of the monthly electricity usage per apartment in Cedar Court was the same as the range of the monthly electricity usage per apartment in Maple Court.
Having the same range also does not determine the average. Two groups can have the same range but different averages. Not sufficient.
(1)+(2) Even together, a greater median and the same range still do not determine which building had the greater average.
Example 1:
• Cedar Court: 4, 5, 6
• Maple Court: 1, 2, 3
Here, Cedar Court has the greater median, and the two groups have the same range. The total usage for Cedar Court is greater than the total usage for Maple Court.
Example 2:
• Cedar Court: 1, 4, 5
• Maple Court: 2, 3, 6
Here, Cedar Court has the greater median, and the two groups have the same range. The total usage for Cedar Court is less than the total usage for Maple Court.
Not sufficient.
Answer: E
