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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Here are the solutions to the problems from the image. 3.1.4. Is f(x) a function on non-function? 3.1.5. Is the graph of f(x) continuous on not continuous? To answer these questions, the definition or graph of f(x) is required. Without this information, it is not possible to determine if f(x) is a function or if its graph is continuous. QUESTION 4.1. Grade 11 B class test marks. The given marks are: 41, 54, 43, 56, 75, 36, 67, 83, 52, 56, 30, 77, 70, 51, 56, 63, 97, 39, 30, 48, 54, 56, 84, 61, 46, 76, 90 There are N = 27 data points. 4.1.1. Arrange the given data in ascending order. Step 1: List all the marks and sort them from smallest to largest. 30, 30, 36, 39, 41, 43, 46, 48, 51, 52, 54, 54, 56, 56, 56, 56, 61, 63, 67, 70, 75, 76, 77, 83, 84, 90, 97 The data in ascending order is: 30, 30, 36, 39, 41, 43, 46, 48, 51, 52, 54, 54, 56, 56, 56, 56, 61, 63, 67, 70, 75, 76, 77, 83, 84, 90, 97 4.1.2. Determine the modal (mode) of the set of data. Step 1: Identify the value that appears most frequently in the sorted data. The number 56 appears 4 times, which is more than any other number. The mode is 56. 4.1.3. Determine the mean of the set of data. Step 1: Sum all the data points. x = 30+30+36+39+41+43+46+48+51+52+54+54+56+56+56+56+61+63+67+70+75+76+77+83+84+90+97 = 1540 Step 2: Divide the sum by the total number of data points (N=27). Mean = ( x)/(N) = (1540)/(27) Step 3: Calculate the value. Mean ≈ 57.037037... The mean is 57.04 (rounded to two decimal places). 4.1.4. Determine the range of the set of data. Step 1: Identify the maximum and minimum values in the data set. Maximum value = 97 Minimum value = 30 Step 2: Calculate the range by subtracting the minimum from the maximum value. Range = Maximum - Minimum = 97 - 30 The range is 67. 4.1.5. Determine the lower quartile (Q_1) and upper quartile (Q_3) of the set of data. Step 1: Find the position of Q_1 using the formula (1)/(4)(N+1). Q_1 position = (1)/(4)(27+1) = (28)/(4) = 7 The 7th value in the sorted list is 46. So, Q_1 = 46. Step 2: Find the position of Q_3 using the formula (3)/(4)(N+1). Q_3 position = (3)/(4)(27+1) = (3 × 28)/(4) = 21 The 21st value in the sorted list is 75. So, Q_3 = 75. The lower quartile (Q_1) is 46 and the upper quartile (Q_3) is 75. 4.1.6. Determine the IQR and the semi-IQR of the set of data. Step 1: Calculate the Interquartile Range (IQR) using the formula IQR = Q_3 - Q_1. IQR = 75 - 46 = 29 Step 2: Calculate the semi-Interquartile Range (semi-IQR) using the formula semi-IQR = (IQR)/(2). semi-IQR = (29)/(2) = 14.5 The IQR is 29 and the semi-IQR is 14.5. 4.2. A class writes a maths test and gets the following marks: 34, 45, 15, 31, 27, 60, 38, 52, 26, 53, 64, 7, 10, 36, 23 4.2.1. Draw a stem and leaf diagram. Step 1: Arrange the data in ascending order. 7, 10, 15, 23, 26, 27, 31, 34, 36, 38, 45, 52, 53, 60, 64 Step 2: Identify the stems (tens digits) and leaves (units digits). Stems: 0, 1, 2, 3, 4, 5, 6 Step 3: Construct the stem and leaf diagram. ` Stem | Leaf -----|----------------- 0 | 7 1 | 0 5 2 | 3 6 7 3 | 1 4 6 8 4 | 5 5 | 2 3 6 | 0 4 Key: 0 | 7 = 7 ` The stem and leaf diagram is shown above. 4.3. The following breeds of dogs are at the SPCA: Husky, Bulldog, Poodle, Husky, Poodle, Bulldog, Poodle, Boxer, Bulldog, Husky, Poodle, Husky, Boxer, Poodle, Poodle Step 1: Tally the frequency of each dog breed. • Husky: Appears 4 times • Bulldog: Appears 3 times • Poodle: Appears 6 times • Boxer: Appears 2 times Total dogs: 4+3+6+2 = 15 Step 2: Create a frequency table. | Dog breed | Tally | Frequency | | :-------- | :---- | :-------- | | Husky | |||| | 4 | | Bulldog | ||| | 3 | | Poodle | ||||| | 6 | | Boxer | || | 2 | | Total | | 15 | Step 3: Calculate the angle for each sector in a pie chart. The total angle in a circle is 360^. • Husky: (4)/(15) × 360^ = 96^ • Bulldog: (3)/(15) × 360^ = 72^ • Poodle: (6)/(15) × 360^ = 144^ • Boxer: (2)/(15) × 360^ = 48^ The completed frequency table and the angles for a pie chart are provided above. 3 done, 2 left today. You're making progress.