1. **State the problem:** We have responses from 30 adults about the convenience they find most difficult to do without: television (T), refrigerator (R), air conditioning (A), public transportation (P), or microwave (M). We need to: prepare frequency distribution, calculate relative frequencies and percentages, find percentage for refrigerator or air conditioning, and describe a bar graph. 2. **Tabulate frequency distribution:** Count each category from the responses: - T: Count the number of T's - R: Count the number of R's - A: Count the number of A's - P: Count the number of P's - M: Count the number of M's Counting each: T = 4 R = 10 A = 7 P = 7 M = 1 3. **Calculate relative frequencies:** Relative frequency is frequency divided by total number of responses (30). - $f_T = \frac{4}{30} = \frac{2}{15} \approx 0.1333$ - $f_R = \frac{10}{30} = \frac{1}{3} \approx 0.3333$ - $f_A = \frac{7}{30} \approx 0.2333$ - $f_P = \frac{7}{30} \approx 0.2333$ - $f_M = \frac{1}{30} \approx 0.0333$ 4. **Calculate percentages:** Multiply relative frequencies by 100 - $P_T = 13.33\%$ - $P_R = 33.33\%$ - $P_A = 23.33\%$ - $P_P = 23.33\%$ - $P_M = 3.33\%$ 5. **Calculate percentage for refrigerator or air conditioning:** Add frequencies for R and A, then find percentage - Total for R and A: $10 + 7 = 17$ - Percentage: $\frac{17}{30} \times 100 = 56.67\%$ 6. **Bar graph description:** The bar graph has categories T, R, A, P, M on the horizontal axis. Vertical axis represents frequency or relative frequency. Each bar height corresponds to the frequency or relative frequency of the category. Final answers: - Frequency Distribution: $T=4$, $R=10$, $A=7$, $P=7$, $M=1$ - Relative Frequencies: $T=0.1333$, $R=0.3333$, $A=0.2333$, $P=0.2333$, $M=0.0333$ - Percentages: $T=13.33\%$, $R=33.33\%$, $A=23.33\%$, $P=23.33\%$, $M=3.33\%$ - Percentage for Refrigerator or Air Conditioning: $56.67\%$