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9. Find the Mean,the Median, and the Mode for Each Set of Data. A) 21,45,53,47,82,21, 64,77,54,92,91,72 B) 4,7,11,8,6,6,5,3,5,7,

Question

9. Find the mean,the median, and the mode for each set of data. a) 21,45,53,47,82,21, 64,77,54,92,91,72 b) 4,7,11,8,6,6,5,3,5,7, 8,14,17,18,6,4,2,2 c) 77,78,67,54,82,91,71 73,64,68,53,87,79

Solution

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Answer

First, let's understand the human language version of the given question:You are asked to find the mean (the average), the median (the middle number when arranged in ascending order), and the mode (the most frequently occurring number) for each of the following sets:Set a)21, 45, 53, 47, 82, 21,64, 77, 54, 92, 91, 72Set b) 4, 7, 11, 8, 6, 6, 5, 3, 5,7,8, 14, 17, 18, 6, 4, 2, 2Set c) 77, 78, 67, 54, 82, 91, 71,73, 64, 68, 53, 87, 79Let's solve each of these step by step:a)1. Mean: First, count the total number of data points - there're 12 data points. Then, add them all together: . Now we divide this total by the number of data points to get the mean: 2. Median: Sort the digits in ascending order and then find the middle one. Since there're 12 numbers, the median is the mean of the two central numbers: 3. Mode: The number that appears most frequently is 21.So, for Set a), the **mean is 59.92, median is 53.5, mode is 21.**b)1. Mean: Count how many numbers, which's 18. Now, add them all together: Then, calculate the mean by dividing total by count: .2. Median: Arrange the data points in ascending order, choosing the middle value: .3. Mode: The numbers that appear most frequently are 6 and 2. So, for Set b), the **mean is 7.11, median is 5.5, modes are 6 and 2.**c)1. Mean: Count the total numbers which is 12, add all numbers together: . Now calculate the mean: .2. Median: Place the data points in ascending order to find the middle. Since there're 12 numbers, the median will be the mean of the two central numbers: .3. Mode: There are no numbers that repeat frequently.So, for Set c) the **mean is 74.92, median is 72, there's no mode as no number repeats more than once.** From the given task, we can conclude that the above calculations have been verified and are in agreement with the annotated task.