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Score: 0 of 5 points Statistics exam scores for students are as follows: \( 92,37,92,58,37,76,48,83,46,56,32,62,42,85,64,35,60,44,61,55,88,63,82,76,92 \). Find the mean and median. (Round your answer to the nearest integer.) Mean: Enter your answer Median: Enter your answer Submit answer Attempts: \( 0 / 1 \) Need help? We apologize, but your instructor has requested that MathGPT not assist with this assignment. But don't be discouraged, you can do it! sil Ackath

Ask by Clarke Lowe. in the United States
Feb 13,2025

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Answer

Mean: 63 Median: 61

Solution

Below is one way to work through the problem: 1. List the scores:   92, 37, 92, 58, 37, 76, 48, 83, 46, 56, 32, 62, 42, 85, 64, 35, 60, 44, 61, 55, 88, 63, 82, 76, 92 2. To find the mean (average), add all the scores and then divide by the number of scores.   • There are 25 scores.   • Summing them in groups:     Group 1: 92 + 37 + 92 + 58 + 37 = 316     Group 2: 76 + 48 + 83 + 46 + 56 = 309     Group 3: 32 + 62 + 42 + 85 + 64 = 285     Group 4: 35 + 60 + 44 + 61 + 55 = 255     Group 5: 88 + 63 + 82 + 76 + 92 = 401   • Total sum = 316 + 309 + 285 + 255 + 401 = 1566   • Mean = 1566 ÷ 25 = 62.64, which rounds to 63. 3. To find the median (the middle score):   • First, sort the scores in increasing order:     32, 35, 37, 37, 42, 44, 46, 48, 55, 56, 58, 60, 61, 62, 63, 64, 76, 76, 82, 83, 85, 88, 92, 92, 92   • Since there are 25 numbers (an odd count), the median is the 13th number.     Counting through the sorted list, the 13th score is 61. Final answers (rounded to the nearest integer):   Mean: 63   Median: 61

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To find the mean, you'll need to add up all the scores and then divide by the number of scores. First, sum the scores: \( 92 + 37 + 92 + 58 + 37 + 76 + 48 + 83 + 46 + 56 + 32 + 62 + 42 + 85 + 64 + 35 + 60 + 44 + 61 + 55 + 88 + 63 + 82 + 76 + 92 = 1,486 \) Next, count the total number of scores, which is 25. Now, calculate the mean: \( \text{Mean} = \frac{1,486}{25} = 59.44 \), rounded to the nearest integer gives you a mean of **59**. For the median, you'll need to organize the scores in ascending order and find the middle number: Sorted scores: \( 32, 35, 37, 37, 42, 44, 46, 48, 55, 56, 58, 60, 61, 62, 63, 64, 76, 76, 82, 83, 85, 88, 92, 92, 92 \). Since there are 25 scores (an odd amount), the median will be the middle score, which is the 13th number in this list: **61**. So, the final answers are: Mean: 59 Median: 61

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