1. **Problem statement:** Calculate mean, median, mode, Q3, D7, P85, and construct FDT, histogram, and bar graph from the given grouped data. 2. **Data:** Rental rate intervals and frequencies (No. of market stalls): 150-179:16, 180-209:9, 210-239:12, 240-269:15, 270-299:35, 300-329:45, 330-359:37, 360-389:35, 390-419:20, 420-449:16 3. **Step 1: Calculate class midpoints ($x_i$):** $$ \begin{aligned} &164.5, 194.5, 224.5, 254.5, 284.5, 314.5, 344.5, 374.5, 404.5, 434.5 \end{aligned} $$ 4. **Step 2: Calculate total frequency ($N$):** $$N = 16 + 9 + 12 + 15 + 35 + 45 + 37 + 35 + 20 + 16 = 240$$ 5. **Step 3: Mean (Method 1 - Direct):** Calculate $\sum f_i x_i$: $$\sum f_i x_i = 16\times164.5 + 9\times194.5 + 12\times224.5 + 15\times254.5 + 35\times284.5 + 45\times314.5 + 37\times344.5 + 35\times374.5 + 20\times404.5 + 16\times434.5 = 72644.5$$ Mean: $$\bar{x} = \frac{\sum f_i x_i}{N} = \frac{72644.5}{240} = 302.69$$ 6. **Step 4: Mean (Method 2 - Assumed mean):** Assume mean $A = 314.5$ (midpoint of 300-329), class width $h=30$. Calculate $d_i = \frac{x_i - A}{h}$ and $f_i d_i$: $$ \begin{aligned} &d_i = [-5, -4, -3, -2, -1, 0, 1, 2, 3, 4] \\ &f_i d_i = 16(-5) + 9(-4) + 12(-3) + 15(-2) + 35(-1) + 45(0) + 37(1) + 35(2) + 20(3) + 16(4) = 12 \end{aligned} $$ Mean: $$\bar{x} = A + h \times \frac{\sum f_i d_i}{N} = 314.5 + 30 \times \frac{12}{240} = 314.5 + 1.5 = 316.0$$ 7. **Step 5: Median:** Median class is where cumulative frequency $\geq \frac{N}{2} = 120$. Cumulative frequencies: 16, 25, 37, 52, 87, 132, 169, 204, 224, 240 Median class: 300-329 (cumulative frequency 132) Median formula: $$\text{Median} = L + \left(\frac{\frac{N}{2} - F}{f_m}\right) \times h$$ Where $L=300$, $F=87$, $f_m=45$, $h=30$ $$\text{Median} = 300 + \left(\frac{120 - 87}{45}\right) \times 30 = 300 + \frac{33}{45} \times 30 = 300 + 22 = 322$$ 8. **Step 6: Mode (Method 1 - Using formula):** Modal class: highest frequency 45 (300-329) $$\text{Mode} = L + \frac{(f_1 - f_0)}{(2f_1 - f_0 - f_2)} \times h$$ Where $L=300$, $f_1=45$, $f_0=35$, $f_2=37$, $h=30$ $$\text{Mode} = 300 + \frac{(45 - 35)}{(2 \times 45 - 35 - 37)} \times 30 = 300 + \frac{10}{18} \times 30 = 300 + 16.67 = 316.67$$ 9. **Step 7: Mode (Method 2 - Using histogram):** Mode is the midpoint of the modal class 300-329, approximately 316.67 as above. 10. **Step 8: Third quartile (Q3):** Position: $\frac{3N}{4} = 180$ Cumulative frequencies show 180 lies in 330-359 class (169 to 204) $$Q3 = L + \left(\frac{\frac{3N}{4} - F}{f}\right) \times h = 330 + \left(\frac{180 - 169}{35}\right) \times 30 = 330 + \frac{11}{35} \times 30 = 330 + 9.43 = 339.43$$ 11. **Step 9: Seventh decile (D7):** Position: $\frac{7N}{10} = 168$ 168 lies in 330-359 class (169 to 204) $$D7 = 330 + \left(\frac{168 - 169}{35}\right) \times 30 = 330 - \frac{1}{35} \times 30 = 330 - 0.86 = 329.14$$ 12. **Step 10: 85th percentile (P85):** Position: $0.85 \times 240 = 204$ 204 lies in 360-389 class (204 to 239) $$P85 = 360 + \left(\frac{204 - 204}{35}\right) \times 30 = 360 + 0 = 360$$ 13. **Step 11: Construct Frequency Distribution Table (FDT):** Already given as intervals and frequencies. 14. **Step 12: Histogram:** Plot rental rate intervals on x-axis and number of stalls on y-axis as vertical bars. 15. **Step 13: Bar graph:** Plot number of stalls for each rental rate interval as rectangular bars with heights proportional to frequencies. **Final answers:** - Mean (Method 1): 302.69 - Mean (Method 2): 316.0 - Median: 322 - Mode (Method 1 & 2): 316.67 - Q3: 339.43 - D7: 329.14 - P85: 360 These calculations provide a comprehensive statistical summary of the rental rate data.