Example Question - median calculation
Here are examples of questions we've helped users solve.
Calculating Mean, Median, and Interquartile Range
In order to solve this question, we need to find the mean, median, and interquartile range of the provided data set: 7, 22, 3, 18, 15, 7, 12, 2, 11, 13, 15, 7, 18 First, let's sort the numbers in ascending order: 2, 3, 7, 7, 7, 11, 12, 13, 15, 15, 18, 18, 22 Now we can calculate each measure: Mean: The mean is calculated by adding all the numbers together and dividing by the count of numbers. Mean = (2 + 3 + 7 + 7 + 7 + 11 + 12 + 13 + 15 + 15 + 18 + 18 + 22) / 13 Mean = 130 / 13 Mean ≈ 10 Median: The median is the middle number of the ordered data set. Since there are 13 numbers, the median will be the 7th number. Median = 12 Interquartile Range (IQR): IQR is the difference between the third quartile (Q3) and the first quartile (Q1). Since we have 13 numbers, the first quartile Q1 will be the median of the first half: Q1 = median of 2, 3, 7, 7, 7, 11 (which is the average of the 3rd and 4th values): Q1 = (7 + 7) / 2 Q1 = 7 The third quartile Q3 will be the median of the second half: Q3 = median of 13, 15, 15, 18, 18, 22 (which is the average of the 3rd and 4th values): Q3 = (15 + 15) / 2 Q3 = 15 IQR = Q3 - Q1 IQR = 15 - 7 IQR = 8 Summary: Mean = ≈10 Median = 12 Interquartile Range = 8
Finding the Median of a Set of Numbers
Dựa vào ảnh bạn cung cấp, đây là một câu hỏi toán học với nội dung: "Cho tập hợp các số tự nhiên có 2 chữ số là {10; 12; 14; 15; 17; 18; 19; 24}. Trung vị của nó là số nào sau đây?" Để tìm trung vị của một tập hợp có số phần tử chẵn, bạn cần sắp xếp tập hợp đó theo thứ tự tăng dần và lấy trung bình cộng của hai số nằm ở giữa tập hợp. Tập hợp đã được cho sẵn theo thứ tự tăng dần là: {10; 12; 14; 15; 17; 18; 19; 24}. Có 8 phần tử trong tập hợp, vì vậy hai số nằm ở giữa là số thứ tư (15) và số thứ năm (17). Tính trung bình cộng của hai số này: (15 + 17) / 2 = 32 / 2 = 16. Vậy, trung vị của tập hợp các số này là 16.
Calculating Interquartile Range
To calculate the interquartile range (IQR), you first need to find the first quartile (Q1), which is the median of the lower half of the data, and the third quartile (Q3), which is the median of the upper half of the data. The interquartile range is the difference between Q3 and Q1. First, we will need to determine the position of the quartiles. There are 11 numbers in the data set you provided: 10, 25, 31, 40, 45, 51, 51, 59, 67, 96, 98 To find Q1, we need the median of the first 5 numbers (since the median - 51 - is not included in either half): 10, 25, 31, 40, 45 The median of these numbers is 31 (the middle number), so Q1 is 31. To find Q3, we take the median of the last 5 numbers: 59, 67, 96, 98 The median of these numbers is the average of 67 and 96 because there are an even number of data points: (67 + 96) / 2 = 163 / 2 = 81.5 So, Q3 is 81.5. Now, find the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 81.5 - 31 = 50.5 Therefore, the interquartile range of the provided data set is 50.5.
Calculating Quartiles
To calculate the lower quartile, median, and upper quartile of the data set provided, here are the steps: 1. Arrange the data in ascending order: 74, 76, 76, 78, 78, 79, 79 2. Determine the median (the middle number): Since there are 7 numbers, the median is the fourth number: 78. 3. Determine the lower quartile (Q1), which is the median of the lower half of the data, not including the median of the dataset. The lower half of the data is 74, 76, 76. The median of this half is the second number: 76. 4. Determine the upper quartile (Q3), which is the median of the upper half of the data, not including the median of the dataset. The upper half of the data is 78, 79, 79. The median of this half is the second number: 79. Therefore, the lower quartile (Q1) is 76, the median is 78, and the upper quartile (Q3) is 79.
Calculating Quartiles of Given Numbers
The image shows a set of numbers in ascending order, and the task is to find the lower quartile, median, and upper quartile of these numbers. Let's calculate each of them: The numbers given are: 13, 23, 34, 37, 45, 47, 52, 56, 58, 66, 81. First, let's find the median, which is the middle number of the data set when arranged in order. Since there are 11 numbers, the median will be the 6th number (as there are 5 numbers on either side of it). So the median is 47. Now let's calculate the lower quartile, which is the median of the lower half of the data set. Exclude the overall median (47) when considering the halves. The lower half of this data set is: 13, 23, 34, 37, 45. The median of this subset is the third number, which is 34, so the lower quartile is 34. Lastly, let's find the upper quartile, which is the median of the upper half of the data set. Again, exclude the overall median (47). The upper half of the data set is: 52, 56, 58, 66, 81. The median of this subset is the third number, which is 58, so the upper quartile is 58. In summary: - The lower quartile is 34. - The median is 47. - The upper quartile is 58.
Statistical Analysis of Numerical Data
The image shows a set of numerical data: 31, 33, 35, 57, 80, 87. To find the lower quartile, median, and upper quartile of this data set, we need to follow these steps: 1. **Median**: Since there are 6 numbers, the median will be the average of the 3rd and 4th numbers. Therefore, the median is (35 + 57) / 2 = 92 / 2 = 46. 2. **Lower Quartile**: The lower quartile (Q1) is the median of the lower half of the data set (excluding the median if the number of observations is odd). With the data set split into two halves (31, 33, 35) and (57, 80, 87), the median of the lower half is 33, since it is the middle value of the first three numbers. 3. **Upper Quartile**: The upper quartile (Q3) is the median of the upper half of the data set (again excluding the median if the number of observations is odd). For the upper half (57, 80, 87), the median is 80, as it is the middle value of the last three numbers. Thus, the lower quartile is 33, the median is 46, and the upper quartile is 80.
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