New Mexico: Population by Age, 2010
| | |
| :-------- | :-------- |
| Under 18 | 518,672 |
| 18-19 | 61,169 |
| 20-24 | 142,370 |
| 25-34 | 267,245 |
| 35-49 | 393,362 |
| 50-64 | 404,106 |
| 65 & over | 272,255 |
| Total | 2,059,179 |
Adapted from U.S. Census Bureau
Which of the following could have been the median age in New Mexico in 2010?
A. 30
B. 32
C. 34
D. 36
Answer (2)
Calculate 50% of the total population: 0.5 × 2 , 059 , 179 = 1 , 029 , 589.5 .
Determine cumulative populations for each age group.
Identify the age group (35-49) where the cumulative population exceeds 1,029,589.5.
Select the answer choice (36) that falls within the 35-49 age range, so the answer is 36 .
Explanation
Understanding the Problem We are given the population distribution by age groups for New Mexico in 2010 and asked to determine which of the given ages could be the median age. The median age is the age that divides the population into two equal halves, meaning 50% of the population is younger and 50% is older.
Calculating 50% of the Total Population First, we need to find 50% of the total population. The total population is 2,059,179. So, 50% of the population is: 0.50 × 2 , 059 , 179 = 1 , 029 , 589.5 This means the median age falls where the cumulative population exceeds 1,029,589.5.
Calculating Cumulative Populations Next, we calculate the cumulative population for each age group:
Under 18: 518,672
Under 20 (Under 18 + 18-19): 518 , 672 + 61 , 169 = 579 , 841
Under 25 (Under 20 + 20-24): 579 , 841 + 142 , 370 = 722 , 211
Under 35 (Under 25 + 25-34): 722 , 211 + 267 , 245 = 989 , 456
Under 50 (Under 35 + 35-49): 989 , 456 + 393 , 362 = 1 , 382 , 818
Under 65 (Under 50 + 50-64): 1 , 382 , 818 + 404 , 106 = 1 , 786 , 924
Total Population: 1 , 786 , 924 + 272 , 255 = 2 , 059 , 179
Identifying the Median Age Group Now we check which age group contains the median age (where the cumulative population exceeds 1,029,589.5):
Under 18: 518,672 (Less than 1,029,589.5)
Under 20: 579,841 (Less than 1,029,589.5)
Under 25: 722,211 (Less than 1,029,589.5)
Under 35: 989,456 (Less than 1,029,589.5)
Under 50: 1,382,818 (Greater than 1,029,589.5) The cumulative population exceeds 1,029,589.5 in the '35-49' age group. Therefore, the median age falls within this group.
Checking the Answer Choices The age group containing the median age is 35-49. Now we check the given answer choices to see which one falls within this range:
A. 30 (Not in the 35-49 range)
B. 32 (Not in the 35-49 range)
C. 34 (Not in the 35-49 range)
D. 36 (In the 35-49 range)
Final Answer Therefore, the only possible median age from the given choices is 36.
Examples
Understanding median age is crucial in urban planning. For instance, if a city's median age is increasing, planners might focus on healthcare and retirement facilities. Conversely, a lower median age might drive investment in schools and family-oriented services. Knowing the age distribution helps allocate resources effectively, ensuring the community's needs are met.
The median age in New Mexico in 2010 falls within the age group of 35-49, indicating that option D. 36 is the correct answer. The cumulative population by age group was calculated to ascertain where it exceeds half of the total population.
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