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07 Aug 2020, 03:47
Kudos
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The answer is E as the median and mean have no relation with each other
Eg. consider a set of the numbers {1,4,5,10,30}. Here the median is 5 and the mean is 10
If we increase the mean by 10% the new mean is 11. and the set can be {10,10,10,10,15} or {1,1,1,1,51} or any 5 values which sum up to 55 and the mean will change for each set
Eg. consider a set of the numbers {1,4,5,10,30}. Here the median is 5 and the mean is 10
If we increase the mean by 10% the new mean is 11. and the set can be {10,10,10,10,15} or {1,1,1,1,51} or any 5 values which sum up to 55 and the mean will change for each set
23 Feb 2026, 21:52
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Your Interpretation:
You read "mean income of a household increases by 10%" as "each household's income increases by 10%."
Why This Interpretation Doesn't Work:
In statistics, "mean" always refers to the AVERAGE of a set, not individual values.
Think of it this way:
- "Mean income of a household" = the average income across ALL households = ONE number
- "Income of each household" = individual household incomes = MANY numbers
If the question wanted to say every household got a 10% raise, it would say:
- "Each household's income increases by 10%", OR
- "All household incomes increase by 10%"
But it says "the mean income" - which is specifically the statistical average.
Simple Example:
Imagine 3 households earning $30K, $50K, and $70K.
- Mean = ($30K + $50K + $70K) / 3 = $50K
- Median = $50K (middle value)
Now, if only the richest household gets a $15K raise:
- New incomes: $30K, $50K, $85K
- New Mean = $55K (increased by 10%!)
- New Median = $50K (unchanged!)
See? The mean increased by 10%, but the median stayed the same. That's why knowing the mean tells us nothing about the median.
Mean and median are independent measures. A change in one does NOT tell us how the other changes - unless we know WHICH values in the set changed.
Since we only know the mean increases (not which specific households' incomes changed), we cannot determine the new median.
Answer: E (Cannot be determined)
You read "mean income of a household increases by 10%" as "each household's income increases by 10%."
Why This Interpretation Doesn't Work:
In statistics, "mean" always refers to the AVERAGE of a set, not individual values.
Think of it this way:
- "Mean income of a household" = the average income across ALL households = ONE number
- "Income of each household" = individual household incomes = MANY numbers
If the question wanted to say every household got a 10% raise, it would say:
- "Each household's income increases by 10%", OR
- "All household incomes increase by 10%"
But it says "the mean income" - which is specifically the statistical average.
Simple Example:
Imagine 3 households earning $30K, $50K, and $70K.
- Mean = ($30K + $50K + $70K) / 3 = $50K
- Median = $50K (middle value)
Now, if only the richest household gets a $15K raise:
- New incomes: $30K, $50K, $85K
- New Mean = $55K (increased by 10%!)
- New Median = $50K (unchanged!)
See? The mean increased by 10%, but the median stayed the same. That's why knowing the mean tells us nothing about the median.
Mean and median are independent measures. A change in one does NOT tell us how the other changes - unless we know WHICH values in the set changed.
Since we only know the mean increases (not which specific households' incomes changed), we cannot determine the new median.
Answer: E (Cannot be determined)
hulk007
