15 1 Two Way Frequency Tables Practice And Problem Solving A B ... - Free Printable

Here is the step-by-step solution to complete your worksheet.

Part 1: Rewrite Frequencies as Relative Frequency (Percent)

To find the relative frequency as a percent, we divide the number in the box by the Grand Total (which is 160) and then multiply by 100. We will round to the nearest whole percent.

Row 1: Inside City Limits
* Electric: $35 \div 160 = 0.21875$ $\rightarrow$ 22%
* Gas: $55 \div 160 = 0.34375$ $\rightarrow$ 34%
* TOTAL: $90 \div 160 = 0.5625$ $\rightarrow$ 56%

Row 2: Outside City Limits
* Electric: $60 \div 160 = 0.375$ $\rightarrow$ 38%
* Gas: $15 \div 160 = 0.09375$ $\rightarrow$ 9%
* TOTAL: $75 \div 160 = 0.46875$ $\rightarrow$ 47%

Column Totals
* Electric TOTAL: $95 \div 160 = 0.59375$ $\rightarrow$ 59%
* Gas TOTAL: $70 \div 160 = 0.4375$ $\rightarrow$ 44%
* GRAND TOTAL: $160 \div 160 = 1.00$ $\rightarrow$ 100%

*(Note: The percentages might not add up perfectly to 100% because of rounding).*

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Part 2: Complete the Joint Relative Frequencies (JRF)

Joint Relative Frequency looks at a specific cell compared to the Grand Total (160).

10. JRF for Electric / Inside City Limits
* Calculation: $35 \div 160$
* Decimal: $0.21875$
* Percent: 22%

11. JRF for Gas / Inside City Limits
* Calculation: $55 \div 160$
* Decimal: $0.34375$
* Percent: 34%

12. JRF for Electric / Outside City Limits
* Calculation: $60 \div 160$
* Decimal: $0.375$
* Percent: 38%

13. JRF for Gas / Outside City Limits
* Calculation: $15 \div 160$
* Decimal: $0.09375$
* Percent: 9%

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Part 3: Name the Marginal Relative Frequencies (MRF)

Marginal Relative Frequency looks at the Totals (the margins of the table) compared to the Grand Total (160).

14. MRF for Electric Total
* Calculation: $95 \div 160$
* Decimal: $0.59375$
* Percent: 59%

15. MRF for Gas Total
* Calculation: $70 \div 160$
* Decimal: $0.4375$
* Percent: 44%

16. MRF for Inside City Limits Total
* Calculation: $90 \div 160$
* Decimal: $0.5625$
* Percent: 56%

17. MRF for Outside City Limits Total
* Calculation: $75 \div 160$
* Decimal: $0.46875$
* Percent: 47%

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Part 4: Calculate Conditional Relative Frequency

Conditional Relative Frequency asks "Out of this specific group, what percent are X?" You divide by the row or column total, not the grand total.

12. Electric, Inside City Limits
* Question: Of the people Inside City Limits (Total 90), how many use Electric (35)?
* Calculation: $35 \div 90$
* Decimal: $0.3888...$
* Percent: 39%

13. Gas, Outside City Limits
* Question: Of the people Outside City Limits (Total 75), how many use Gas (15)?
* Calculation: $15 \div 75$
* Decimal: $0.20$
* Percent: 20%

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Final Answer:

Table Values (Relative Frequency %):
* Inside/Electric: 22% | Inside/Gas: 34% | Inside/Total: 56%
* Outside/Electric: 38% | Outside/Gas: 9% | Outside/Total: 47%
* Total/Electric: 59% | Total/Gas: 44% | Grand Total: 100%

Joint Relative Frequencies (JRF):
10. 22%
11. 34%
12. 38%
13. 9%

Marginal Relative Frequencies (MRF):
14. 59%
15. 44%
16. 56%
17. 47%

Conditional Relative Frequency:
12. 39%
13. 20%