This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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For Questions 9 - 11: We will use the provided table for "HEIGHT OF SELECTED STUDENTS AT XYZ SCHOOL". Step 1: Determine the value of 'a'. The value 'a' represents the "Less than cumulative frequency" for the class 130 h < 140. This is the sum of the frequencies of the current class and all preceding classes. a = Frequency(120 h < 130) + Frequency(130 h < 140) a = 8 + 12 = 20 9. What must be the value of a in the table? Answer: 20 Step 2: Determine the value of 'b'. The value 'b' represents the "Greater than cumulative frequency" for the class 140 h < 150. This is the sum of the frequencies of the current class and all succeeding classes. b = Frequency(140 h < 150) + Frequency(150 h < 160) + Frequency(160 h < 170) b = 14 + 7 + 9 = 30 Alternatively, the "Greater than cumulative frequency" for 130 h < 140 is 42. Subtracting the frequency of this class (12) gives 'b'. b = 42 - 12 = 30 10. What must be the value b in the table? Answer: 30 Step 3: Find the number of students standing less than 160 cm. This value is directly given in the "Less than cumulative frequency" column for the class 150 h < 160. From the table, the "Less than cumulative frequency" for 150 h < 160 is 41. 11. How many students stand less than 160 cm? Answer: 41 For Question 12: We need to complete the table by calculating the Midpoint and Relative frequency (%) for each class interval, rounding to the nearest hundredths. Step 4: Calculate the total frequency. First, sum all the frequencies to find the total number of data points. Total Frequency = 8 + 14 + 13 = 35 Step 5: Calculate the Midpoint for each class interval. The midpoint is calculated as Lower Limit + Upper Limit2. For 20-24: (20 + 24)/(2) = (44)/(2) = 22 (Matches given) For 25-29: (25 + 29)/(2) = (54)/(2) = 27 For 30-34: (30 + 34)/(2) = (64)/(2) = 32 Step 6: Calculate the Relative frequency (%) for each class interval. Relative frequency (%) is calculated as FrequencyTotal Frequency × 100\%. For 20-24: (8)/(35) × 100\% ≈ 22.857\% ≈ 22.86\% (Matches given) For 25-29: (14)/(35) × 100\% = (2)/(5) × 100\% = 0.4 × 100\% = 40.00\% For 30-34: (13)/(35) × 100\% ≈ 37.142\% ≈ 37.14\% 12. Complete the table below: (Round off decimal answers to the nearest hundredths) Answer: | Class Interval | Frequency | Midpoint | Relative frequency (%) | | :------------- | :-------- | :------- | :--------------------- | | 20-24 | 8 | 22 | 22.86 | | 25-29 | 14 | 27 | 40.00 | | 30-34 | 13 | 32 | 37.14 | Last free one today — make it count tomorrow, or type /upgrade for unlimited.