Example Question - lower quartile calculation
Here are examples of questions we've helped users solve.
Calculating Quartiles for a Data Set
To find the lower quartile, median, and upper quartile for the given data set, we follow these steps: 1. Median: This is the middle value when the data set is ordered from smallest to largest. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values. The given data set is already ordered: 1, 2, 2, 2, 3, 3, 6, 8, 8 There are 9 values, so the middle one will be the 5th value (since (9 + 1) / 2 = 5): 1, 2, 2, 2, 3, 3, 6, 8, 8 Hence, the median is 3. 2. Lower Quartile (Q1): This is the median of the lower half of the data (excluding the median if the number of values is odd). For our data set, the lower half (before the median) is: 1, 2, 2, 2 In this set of 4 values, the lower quartile is the average of the 2nd and 3rd value (because (4 + 1) / 2 = 2.5, which means we take the average of 2nd and 3rd): (2 + 2) / 2 = 4 / 2 = 2 Hence, the lower quartile is 2. 3. Upper Quartile (Q3): This is the median of the upper half of the data (excluding the median if the number of values is odd). For our data set, the upper half (after the median) is: 3, 6, 8, 8 In this set of 4 values, the upper quartile is the average of the 6 and 8: (6 + 8) / 2 = 14 / 2 = 7 Hence, the upper quartile is 7. In summary: - Lower Quartile (Q1) = 2 - Median = 3 - Upper Quartile (Q3) = 7
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 from a Dataset
To find the lower quartile, median, and upper quartile from a set of numbers, you first ensure that the numbers are ordered from smallest to largest, which they already are in the image you provided: 14, 20, 20, 31, 38, 45, 54, 81, 81, 87, 92 There are 11 numbers in this dataset. The median (the middle number) is easy to find because there is an odd number of data points. The median will be the value in the middle of the dataset: Median: Since there are 11 numbers, the median will be the 6th number (as 5 numbers are on either side): 14, 20, 20, 31, 38, (45), 54, 81, 81, 87, 92 So, the median is 45. For the quartiles, we divide the dataset into four equal parts. The lower quartile (Q1) is the median of the lower half of the dataset (not including the median if there is an odd number of data points), and the upper quartile (Q3) is the median of the upper half of the dataset. Lower quartile: The lower half of the dataset (before the median) is: 14, 20, 20, 31, 38 Since there are 5 numbers in this lower half, the lower quartile is the middle value, which is the 3rd number: 14, 20, (20), 31, 38 So, the lower quartile is 20. Upper quartile: The upper half of the dataset (after the median) is: 54, 81, 81, 87, 92 Again, there are 5 numbers in this upper half, so the upper quartile will also be the middle value, which is the 3rd number: 54, 81, (81), 87, 92 So, the upper quartile is 81. In summary: Lower quartile (Q1) = 20 Median (Q2) = 45 Upper quartile (Q3) = 81
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com