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
here are the solutions to your questions: For Question 12: Step 1: Count the frequency of each score in the given set. The scores are: 2, 4, 3, 5, 2, 5, 3, 2, 4, 2, 3, 4, 4. Count of 2: 4 times Count of 3: 3 times Count of 4: 4 times Count of 5: 2 times Step 2: Identify the score(s) with the highest frequency. The highest frequency is 4, which occurs for both score 2 and score 4. 12. What is/are the mode(s) of the following set of scores? Answer: 2, 4 For Questions 13 - 15: Assumption: The table provided has a typo. Given that the problem refers to "50 students" and the sum of the frequencies 8+12+7+10+13 = 50, it is assumed that the second entry for 'Grade 97' (with 7 students) should be 'Grade 94' to make the grades distinct and complete the distribution for 50 students. The corrected table used for calculations is: | Grade (x) | Number of Students (f) | | :-------- | :--------------------- | | 98 | 8 | | 97 | 12 | | 96 | 10 | | 95 | 13 | | 94 | 7 | | Total | N = 50 | Step 1: Calculate the mean score (Question 13). To find the mean of grouped data, we use the formula Mean = ( fx)/(N), where f is the frequency (number of students) and x is the grade. 98 × 8 = 784 97 × 12 = 1164 96 × 10 = 960 95 × 13 = 1235 94 × 7 = 658 fx = 784 + 1164 + 960 + 1235 + 658 = 4801 N = 50 Mean = (4801)/(50) = 96.02 13. What is the mean score of the 50 students? Answer: 96.02 Step 2: Calculate the median score (Question 14). First, find the position of the median. Since there are N=50 students (an even number), the median is the average of the (N)/(2)-th and ((N)/(2) + 1)-th values. (50)/(2) = 25-th value (50)/(2) + 1 = 26-th value Next, create a cumulative frequency (cf) column for the corrected table: Grade 98: cf = 8 Grade 97: cf = 8 + 12 = 20 Grade 96: cf = 20 + 10 = 30 The 25th and 26th scores both fall within the 'Grade 96' category (since the cumulative frequency reaches 20 at Grade 97, and 30 at Grade 96, meaning scores from 21st to 30th are 96). Therefore, both the 25th and 26th scores are 96. Median = (96 + 96)/(2) = 96 14. What is the median score of the set of scores? Answer: 96 Step 3: Calculate the mode score (Question 15). The mode is the grade with the highest frequency (number of students). From the corrected table: Grade 98: 8 students Grade 97: 12 students Grade 96: 10 students Grade 95: 13 students Grade 94: 7 students The highest frequency is 13, which corresponds to Grade 95. 15. What is the mode of the set of scores? Answer: 95 Last free one today — make it count tomorrow, or type /upgrade for unlimited.