Question

complete the frequency table and answer the following questions.
census figures showing household incomes, in dollars, in a neighborhood:

class interval	tally	frequency	absolute cumulative frequency	(%) relative frequency	relative cumulative frequency
25,000 - 40,000			7	10
40,000 - 55,000			16	26
55,000 - 70,000			12	38
70,000 - 85,000			6	44
85,000 - 100,000			4	48
> 100,000			2	50

1. which interval occurs most frequently?
2. how many households had incomes between $55,000 and $70,000?
3. how many households had incomes between $55,000 and $85,000?
4. how many households had incomes below $85,000?
5. what percentage of households made below $70,000?
6. what percentage of households made above $70,000?
7. what percentage of households made above $85,000?
8. what percentage of households made above $55,000?
9. what percentage made between $55,000 and $70,000?
10. what percentage made between $40,000 and $70,000?

mathnasium llc copyright 2007 focus_on_fq_060_frq_tbl_hstgrm_v03 - 14

Explanation:

Step1: Calculate total number of households

Sum of absolute frequencies: $3 + 7+16 + 12+6 + 4+2=50$

Step2: Complete cumulative frequencies

For $40,000 - 55,000$, cumulative frequency is $3 + 7+16 = 26$.

Step3: Calculate relative frequencies

Relative frequency of a class = $\frac{\text{Absolute frequency}}{\text{Total frequency}}\times100\%$
For $<25,000$: $\frac{3}{50}\times100\% = 6\%$
For $25,000 - 40,000$: $\frac{7}{50}\times100\% = 14\%$
For $40,000 - 55,000$: $\frac{16}{50}\times100\% = 32\%$
For $55,000 - 70,000$: $\frac{12}{50}\times100\% = 24\%$
For $70,000 - 85,000$: $\frac{6}{50}\times100\% = 12\%$
For $85,000 - 100,000$: $\frac{4}{50}\times100\% = 8\%$
For $>100,000$: $\frac{2}{50}\times100\% = 4\%$

Step4: Calculate cumulative relative frequencies

For $<25,000$: $6\%$
For $25,000 - 40,000$: $6\%+14\% = 20\%$
For $40,000 - 55,000$: $20\%+32\% = 52\%$
For $55,000 - 70,000$: $52\%+24\% = 76\%$
For $70,000 - 85,000$: $76\%+12\% = 88\%$
For $85,000 - 100,000$: $88\%+8\% = 96\%$
For $>100,000$: $96\%+4\% = 100\%$

Step5: Answer questions

1. The interval $40,000 - 55,000$ has the highest absolute frequency of $16$, so it occurs most frequently.
2. The number of households with incomes between $\$55,000$ and $\$70,000$ is $12$.
3. The number of households with incomes between $\$55,000$ and $\$85,000$ is $12 + 6=18$.
4. The number of households with incomes below $\$85,000$ is $3+7 + 16+12+6=44$.
5. The percentage of households with incomes below $\$70,000$ is $76\%$.
6. The percentage of households with incomes above $\$70,000$ is $100 - 76=24\%$.
7. The percentage of households with incomes above $\$85,000$ is $8 + 4=12\%$.
8. The percentage of households with incomes above $\$55,000$ is $24+12+8 + 4=48\%$.
9. The percentage of households with incomes between $\$55,000$ and $\$70,000$ is $24\%$.
10. The percentage of households with incomes between $\$40,000$ and $\$70,000$ is $32+24 = 56\%$.

Answer:

1. $40,000 - 55,000$
2. $12$
3. $18$
4. $44$
5. $76\%$
6. $24\%$
7. $12\%$
8. $48\%$
9. $24\%$
10. $56\%$