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Originally posted by Sajjad1994 on 09 May 2021, 21:00.
Last edited by BottomJee on 02 Feb 2024, 00:29, edited 4 times in total.
Last edited by BottomJee on 02 Feb 2024, 00:29, edited 4 times in total.
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The median household size of all households in the five states combined is two people.: True
Of the seven categories of household size, Maine has the median number of households in exactly three.: False
In each of the seven categories of household size, Massachusetts has more households than the next highest two states combined.: True
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Household Size: Occupied Housing Units by State, 2010 Census
The above data are drawn from 2010 census data for New England (excluding Rhode Island, whose data is not available). The table provides the total number of households in each state and the distribution of households of various sizes within each state.
Consider the following statements about these states. For each statement, evaluate whether that statement is True or False, according to the information in the table.
(Sort ↕ the table by clicking on the headers)
| -------------- | 1-person households | 2-person households | 3-person households | 4-person households | 5-person households | 6-person households | 7 or more person households | Total households |
|---|---|---|---|---|---|---|---|---|
| Connecticut | 373648 | 443095 | 226658 | 197116 | 84916 | 29348 | 16306 | 1371087 |
| Maine | 159533 | 213695 | 84340 | 64010 | 23840 | 7854 | 3947 | 557219 |
| Massachusetts | 732263 | 813166 | 417216 | 353676 | 150842 | 51409 | 28503 | 2547075 |
| New Hampshire | 133057 | 188923 | 85046 | 70835 | 27365 | 9286 | 4461 | 518973 |
| Vermont | 72233 | 96889 | 39695 | 31210 | 11107 | 3480 | 1828 | 256442 |
The above data are drawn from 2010 census data for New England (excluding Rhode Island, whose data is not available). The table provides the total number of households in each state and the distribution of households of various sizes within each state.
Consider the following statements about these states. For each statement, evaluate whether that statement is True or False, according to the information in the table.
| True | False | |
| The median household size of all households in the five states combined is two people. | ||
| Of the seven categories of household size, Maine has the median number of households in exactly three. | ||
| In each of the seven categories of household size, Massachusetts has more households than the next highest two states combined. |
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Official Answer
The median household size of all households in the five states combined is two people.: True
Of the seven categories of household size, Maine has the median number of households in exactly three.: False
In each of the seven categories of household size, Massachusetts has more households than the next highest two states combined.: True
18 May 2021, 00:59
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Official Explanation
The median household size of all households in the five states combined is two people.
Now you’re being asked to determine the median household size for all states combined. To do this, first sum up the total number of households for all five states (the far right column). Rounding to the nearest thousand, you get 1,000 × (1,371 + 557 + 2,547 + 519 + 256) = 5,250,000. That means that if you were to place all these households in order according to their size, the median household would be roughly the \(\frac{5,250,000}{2} =\) 2,625,000th household. The household size of the 2,625,000th household is therefore the median household size.
To determine the size of that particular household, you need to total the number of households of each size until you hit the 2.6-million mark. Starting at either end of the table will eventually get you to the middle, but because there are bigger numbers of smaller households, you’ll reach the threshold faster if you start on the left with the one-person households. Rounding to the thousands place gets you 1,000 × (374 + 160 + 732 + 133 + 72) = 1,471,000, so you’re a little over halfway to the 2,625,000th house.
Careful observation saves even more work on the next step of finding this solution. Every state has more two-person households than one-person households. If you actually tallied up the exact number of one- and two-person households, you’d end up with a number well above 2,900,000 (twice the previous total). Therefore, the 2,625,000th household must be a two-person household, so this statement can be marked “True.”
Of the seven categories of household size, Maine has the median number of households in exactly three.
This is another question about medians. You need to find the median number for each of the seven categories and determine whether Maine has the median for exactly three of them. It’s time to use the Sort function again.
One-person households:
Maine is the median for one-person households. That’s one instance so far.
Two-person households:
Maine is again the median; that makes two instances.
Three-person households:
New Hampshire is the median; keep going.
Four-person households:
New Hampshire again; not what you’re looking for.
Five-person households:
Still New Hampshire.
Six-person households:
New Hampshire is the median frequently in this table. There’s only one more chance to find a third instance of Maine being the median.
Seven-or-more-person households:
No luck. The median is once again New Hampshire.
Maine is the median in exactly two of the seven categories, making the answer to this statement “False.” Note that Maine is the median of the “Total” column, so there are actually three instances in the table in which Maine is the median. However, this question asks only for the seven categories, not all columns. Pay close attention to each column heading as you work through Table Analysis questions.
In each of the seven categories of household size, Massachusetts has more households than the next highest two states combined.
From your first glance at the table, you noticed that Massachusetts has by far the largest total number of households. So you can guess that Massachusetts might be the greatest in every subcategory. You can sort the tables as before to determine the rankings of the states in each column. For each one, you need to determine whether the number of households in Massachusetts is greater than the second-highest state plus the third-highest state. Perform the calculation for each household-size category and, where possible, use approximation instead of calculation:
Since Massachusetts is higher than the next highest two states combined in each category, the answer here is “True.” Note that you did not need to perform the exact calculations for any of those comparisons; once you identified the correct values to compare, you could estimate the sum of the second-highest state plus the third-highest state and see that in each case, it is less than the number of households in Massachusetts.
The median household size of all households in the five states combined is two people.
Now you’re being asked to determine the median household size for all states combined. To do this, first sum up the total number of households for all five states (the far right column). Rounding to the nearest thousand, you get 1,000 × (1,371 + 557 + 2,547 + 519 + 256) = 5,250,000. That means that if you were to place all these households in order according to their size, the median household would be roughly the \(\frac{5,250,000}{2} =\) 2,625,000th household. The household size of the 2,625,000th household is therefore the median household size.
To determine the size of that particular household, you need to total the number of households of each size until you hit the 2.6-million mark. Starting at either end of the table will eventually get you to the middle, but because there are bigger numbers of smaller households, you’ll reach the threshold faster if you start on the left with the one-person households. Rounding to the thousands place gets you 1,000 × (374 + 160 + 732 + 133 + 72) = 1,471,000, so you’re a little over halfway to the 2,625,000th house.
Careful observation saves even more work on the next step of finding this solution. Every state has more two-person households than one-person households. If you actually tallied up the exact number of one- and two-person households, you’d end up with a number well above 2,900,000 (twice the previous total). Therefore, the 2,625,000th household must be a two-person household, so this statement can be marked “True.”
Of the seven categories of household size, Maine has the median number of households in exactly three.
This is another question about medians. You need to find the median number for each of the seven categories and determine whether Maine has the median for exactly three of them. It’s time to use the Sort function again.
One-person households:
Maine is the median for one-person households. That’s one instance so far.
Two-person households:
Maine is again the median; that makes two instances.
Three-person households:
New Hampshire is the median; keep going.
Four-person households:
New Hampshire again; not what you’re looking for.
Five-person households:
Still New Hampshire.
Six-person households:
New Hampshire is the median frequently in this table. There’s only one more chance to find a third instance of Maine being the median.
Seven-or-more-person households:
No luck. The median is once again New Hampshire.
Maine is the median in exactly two of the seven categories, making the answer to this statement “False.” Note that Maine is the median of the “Total” column, so there are actually three instances in the table in which Maine is the median. However, this question asks only for the seven categories, not all columns. Pay close attention to each column heading as you work through Table Analysis questions.
In each of the seven categories of household size, Massachusetts has more households than the next highest two states combined.
From your first glance at the table, you noticed that Massachusetts has by far the largest total number of households. So you can guess that Massachusetts might be the greatest in every subcategory. You can sort the tables as before to determine the rankings of the states in each column. For each one, you need to determine whether the number of households in Massachusetts is greater than the second-highest state plus the third-highest state. Perform the calculation for each household-size category and, where possible, use approximation instead of calculation:
- One-person households: Is 732,263 > 373,648 + 159,533? Yes.
- Two-person households: Is 813,166 > 443,095 + 213,695? Yes.
- Three-person households: Is 417,216 > 226,658 + 85,046? Yes.
- Four-person households: Is 353,676 > 197,116 + 70,835? Yes.
- Five-person households: Is 150,842 > 84,916 + 27,365? Yes.
- Six-person households: Is 51,409 > 29,348 + 9,286? Yes.
- Seven-or-more-person households: Is 28,503 > 16,306 + 4,461? Yes.
Since Massachusetts is higher than the next highest two states combined in each category, the answer here is “True.” Note that you did not need to perform the exact calculations for any of those comparisons; once you identified the correct values to compare, you could estimate the sum of the second-highest state plus the third-highest state and see that in each case, it is less than the number of households in Massachusetts.
