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.
ScanSolve AI Answer
tahellemadenko01, let's knock this out. First, I will list the heights from the image. I can identify 32 heights from the provided image. Although the question states "42 students", I will proceed with the 32 visible data points and note this assumption. The heights are: 155, 134, 164, 174, 126, 158, 168, 162, 142, 154, 159, 179, 137, 157, 166, 151, 136, 145, 173, 168, 157, 163, 165, 152, 140, 169, 154, 167, 171, 157, 160, 158. Sorting these heights in ascending order: 126, 134, 136, 137, 140, 142, 145, 151, 152, 154, 154, 155, 157, 157, 157, 158, 158, 159, 160, 162, 163, 164, 165, 166, 167, 168, 168, 169, 171, 173, 174, 179. a) Grouping the height in intervals of 10cm, starting at 120cm. Construct the Cumulative Frequency Table for the data. Step 1: Define the class intervals. The intervals are 10cm wide, starting at 120cm. 120 & height < 130 \\ 130 & height < 140 \\ 140 & height < 150 \\ 150 & height < 160 \\ 160 & height < 170 \\ 170 & height < 180 Step 2: Count the frequency for each interval. • 120 - 129 cm: 126 (1 student) • 130 - 139 cm: 134, 136, 137 (3 students) • 140 - 149 cm: 140, 142, 145 (3 students) • 150 - 159 cm: 151, 152, 154, 154, 155, 157, 157, 157, 158, 158, 159 (11 students) • 160 - 169 cm: 160, 162, 163, 164, 165, 166, 167, 168, 168, 169 (10 students) • 170 - 179 cm: 171, 173, 174, 179 (4 students) Step 3: Construct the Cumulative Frequency Table. |c|c|c| Height (cm) & Frequency (f) & Cumulative Frequency (cf) \\ 120 - 129 & 1 & 1 \\ 130 - 139 & 3 & 1 + 3 = 4 \\ 140 - 149 & 3 & 4 + 3 = 7 \\ 150 - 159 & 11 & 7 + 11 = 18 \\ 160 - 169 & 10 & 18 + 10 = 28 \\ 170 - 179 & 4 & 28 + 4 = 32 \\ b) Students who are shorter than 150cm pay half price to enter a team park. How many of these students are there? Step 1: Identify the heights shorter than 150cm. This includes all students in the height intervals below 150cm. These are the students in the 120-129 cm, 130-139 cm, and 140-149 cm intervals. Step 2: Sum the frequencies for these intervals. Number of students = (Frequency for 120-129 cm) + (Frequency for 130-139 cm) + (Frequency for 140-149 cm) Number of students = 1 + 3 + 3 = 7 Alternatively, from the cumulative frequency table, the cumulative frequency for the "140 - 149" class is 7, which represents all students with heights less than 150 cm. There are 7 students who are shorter than 150cm. What's next?