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
Step 1: List the given data in ascending order. The weights of the 30 learners are: 22, 14, 18, 26, 32, 11 29, 21, 15, 27, 34, 13 24, 19, 20, 25, 25, 21 10, 16, 28, 20, 17, 24 12, 19, 22, 25, 33, 21 Sorted data: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 19, 20, 20, 21, 21, 21, 22, 22, 24, 24, 25, 25, 25, 26, 27, 28, 29, 32, 33, 34 i) Construct a frequency distribution table. Using class intervals of 10-14, 15-19, 20-24, etc., we calculate the frequency (f), midpoint (x), product of frequency and midpoint (fx), and cumulative frequency (cf) for each class. | Class Interval | Frequency (f) | Midpoint (x) | fx | Cumulative Frequency (cf) | |:---------------|:--------------|:-------------|:---|:--------------------------| | 10-14 | 5 | 12 | 60 | 5 | | 15-19 | 6 | 17 | 102| 11 | | 20-24 | 9 | 22 | 198| 20 | | 25-29 | 7 | 27 | 189| 27 | | 30-34 | 3 | 32 | 96 | 30 | | Total | f = 30 | | fx = 645 | | ii) Identify the modal class. The modal class is the class interval with the highest frequency. From the table, the highest frequency is 9, which corresponds to the class interval 20-24. The modal class is 20-24. iii) Calculate the mean weight of the learners. The mean (x) for grouped data is calculated using the formula: x = ( fx)/( f) From the frequency distribution table: fx = 645 f = 30 Substitute these values into the formula: x = (645)/(30) x = 21.5 The mean weight of the learners is 21.5. iv) Determine the median class. The median class is the class interval where the median value lies. The total number of learners (N) is 30. The position of the median is (N)/(2) = (30)/(2) = 15^th value. Looking at the cumulative frequency column: • The 5th value is in the 10-14 class. • The 11th value is in the 15-19 class. • The 20th value is in the 20-24 class. Since the 15th value falls between the 11th and 20th values, it is located in the 20-24 class. The median class is 20-24. That's 2 down. 3 left today — send the next one.