Example Question - lower quartile
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Calculating Quartiles
To solve for the lower quartile, median, and upper quartile, you first need to arrange the data in ascending order, which appears to be already done in the image: 74, 76, 76, 78, 78, 79, 79. The median (or second quartile) is the middle number of a data set that's been arranged in order, and since there are seven numbers, the middle one is the fourth one: 78. For odd-numbered data sets, the lower quartile (or first quartile, Q1) is the median of the first half of the data not including the overall median. The first half of the data is 74, 76, 76, so the lower quartile is the middle of these three numbers, which is 76. The upper quartile (or third quartile, Q3) is the median of the second half of the data not including the overall median. The second half of the data is 78, 79, 79, so the upper quartile is the middle of these three numbers, which is 79. Therefore, the lower quartile is 76, the median is 78, and the upper quartile is 79.
Statistical Analysis of a Number Set
In the image, you're provided with a set of numbers: 2, 6, 6, 7, 9. To find the lower quartile, median, and upper quartile of these numbers, we need to follow some statistical steps. The median (also called the second quartile) is the middle number when the numbers are ordered from lowest to highest. Here, the numbers are already sorted, so the median is the middle number in the set. Median = the third number in the list = 6. The lower quartile (also called the first quartile) is the median of the lower half of the data set (not including the median if the number of observations is odd). In this case, the lower half of the data set is 2 and 6. Lower quartile = the median of the lower half = (2 + 6) / 2 = 8 / 2 = 4. The upper quartile (also called the third quartile) is the median of the upper half of the data set (again, not including the median if the number of observations is odd). The upper half of the set here is 7 and 9. Upper quartile = the median of the upper half = (7 + 9) / 2 = 16 / 2 = 8. So, for the given set of numbers, the lower quartile is 4, the median is 6, and the upper quartile is 8.
Calculating Quartiles from Sorted Data
To solve for the lower quartile, median, and upper quartile, we first need to arrange the data in ascending order, which is already done for us: 2, 6, 6, 7, 9. The median is the middle number when the data is ordered from least to greatest. In this case, since there are five numbers, the median will be the third number: Median = 6 The lower quartile (Q1) is the median of the lower half of the data. Since there are 5 data points, we will consider the lower half to be the first two numbers (2 and 6). The median of these two numbers is: Lower quartile = (2 + 6) / 2 = 8 / 2 = 4 The upper quartile (Q3) is the median of the upper half of the data. For the upper half, we take the last two numbers (7 and 9). The median of these is: Upper quartile = (7 + 9) / 2 = 16 / 2 = 8 Now we have our three values: - Lower quartile = 4 - Median = 6 - Upper quartile = 8
Finding Quartiles of a Dataset
To solve the question, we need to find the lower quartile, median, and upper quartile of the given data set. Let's first arrange the data in order: 14, 20, 31, 38, 45, 54, 81, 87, 92 From the image, it's clear that the data is already sorted in ascending order. There are nine numbers in the series, so the median (the middle value) will be the fifth number: Median = 45 The lower quartile (Q1) is the median of the lower half of the data, excluding the median of the entire set if the size is an odd number, so we look at the first four numbers: 14, 20, 31, 38 The median of these four numbers is the average of the middle two values: Lower quartile (Q1) = (20 + 31) / 2 = 51 / 2 = 25.5 The upper quartile (Q3) is the median of the upper half of the data, excluding the median of the entire set. We consider the last four numbers: 54, 81, 87, 92 The median of these four numbers is the average of the middle two values: Upper quartile (Q3) = (81 + 87) / 2 = 168 / 2 = 84 So, the lower quartile is 25.5, the median is 45, and the upper quartile is 84.
Calculating Quartiles from a Set of Numbers
The image presents a set of numbers and asks to find the lower quartile, median, and upper quartile. The numbers in the set are: 13, 25, 34, 37, 45, 47, 52, 56, 58, 66, 81 The median is the middle number when the numbers are ordered from least to greatest. Since there are 11 numbers, the median is the 6th number in the list. Let's find it: Median = 47 Quartiles divide the data into four equal parts. The lower quartile (Q1) is the median of the lower half of the data, and the upper quartile (Q3) is the median of the upper half. For the lower quartile, we'll consider the numbers before the median: 13, 25, 34, 37, 45 Since there are 5 numbers, the lower quartile is the middle one, which is the 3rd number: Lower quartile (Q1) = 34 For the upper quartile, we take the numbers after the median: 52, 56, 58, 66, 81 Similarly, since there are 5 numbers, the upper quartile is the middle one, which is the 3rd number in this set: Upper quartile (Q3) = 58 To summarize: Lower quartile (Q1) = 34 Median = 47 Upper quartile (Q3) = 58
Calculating Quartiles from Sorted Data Set
The image shows a list of numbers, which we'll assume is a data set that is sorted in ascending order. The task is to find the lower quartile, median, and upper quartile of the data. First, let's count how many data points there are: 13, 25, 34, 37, 45, 47, 52, 56, 58, 66, 81 There are 11 numbers in this data set. The median is the middle number when the data is ordered from least to greatest, which is the (11 + 1) / 2 = 6th number. Therefore, the median is the value of the 6th data point, which is 47. To find the quartiles, we will look at the data below and above the median: Lower half (excluding the median): 13, 25, 34, 37, 45 Upper half (excluding the median): 52, 56, 58, 66, 81 Each half has 5 numbers. The lower quartile (Q1) is the median of the lower half, and the upper quartile (Q3) is the median of the upper half. For 5 numbers, the median will be the 3rd number in order (since it's the middle number): (5 + 1) / 2 = 3rd number. For the lower half: The lower quartile (Q1) is the 3rd data point of the lower half, which is 34. For the upper half: The upper quartile (Q3) is the 3rd data point of the upper half, which is 58. So the answers are: - Lower quartile = 34 - Median = 47 - Upper quartile = 58
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 Quartiles Calculation
The image shows a list of numbers: 31, 33, 35, 57, 80, 87. To find the lower quartile, median, and upper quartile, follow these steps: 1. **Median:** Since there are 6 numbers, the median will be the average of the 3rd and 4th numbers, which are 35 and 57. \[ \text{Median} = \frac{35 + 57}{2} = \frac{92}{2} = 46 \] 2. **Lower Quartile (Q1):** For an even set of numbers, the lower quartile is the median of the lower half of the data (not including the median if the data set count is odd). The lower half of the data set is 31, 33, 35. Since there are three numbers, the middle one is the median. Thus, the lower quartile is 33. 3. **Upper Quartile (Q3):** Similarly for the upper quartile, which is the median of the upper half of the data, the upper half is 57, 80, 87. Again, because there are three numbers, the middle one is the median of this subset. So, the upper quartile is 80. Therefore, the lower quartile is 33, the median is 46, and the upper quartile is 80.
Statistical Data Analysis
This exercise is about finding the lower quartile, median, and upper quartile of the given set of numbers. The given dataset is already arranged in ascending order: 31, 33, 35, 57, 80, 87. To find the median (which is also the second quartile), we find the middle value of the dataset. Since there are an even number of data points (6 numbers), the median will be the average of the two middle numbers (35 and 57). Median = (35 + 57) / 2 = 92 / 2 = 46 Now, to find the lower quartile (first quartile), we take the median of the lower half of the dataset. The lower half (before the median value) is 31, 33, 35. Since there are three numbers, the middle one is the lower quartile. Lower quartile = 33 To find the upper quartile (third quartile), we take the median of the upper half of the dataset. The upper half (after the median value) is 57, 80, 87. Since there are three numbers here as well, the middle one is the upper quartile. Upper quartile = 80 Therefore, the lower quartile is 33, the median is 46, and the upper quartile is 80.
Calculating Quartiles in a Data Set
To find the lower quartile, median, and upper quartile of a data set, we'll follow these steps: 1. **Median**: The median is the middle value of a data set when it's ordered from least to greatest. If the number of data points is odd, the median is the middle number. If it's even, the median is the average of the two middle numbers. For this set, there is an odd number of data points (7), so the median is the value in the middle - the fourth data point: \( \text{Median} = 35 \) 2. **Lower Quartile (Q1)**: The lower quartile is the median of the lower half of the data set (not including the median if the number of data points is odd). In this case, it's the median of the first three numbers: \( \text{Lower quartile} = 26 \) (as it is the middle of the first three numbers: 10, 26, 35) 3. **Upper Quartile (Q3)**: The upper quartile is the median of the upper half of the data set (again, not including the median if the number of data points is odd). The upper half of this data set is the last three numbers: \( \text{Upper quartile} = 55 \) (as it is the middle of the last three numbers: 43, 55, 73) To summarize: - **Lower Quartile**: 26 - **Median**: 35 - **Upper Quartile**: 55
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