Example Question - quartiles
Here are examples of questions we've helped users solve.
Calculating Interquartile Range
The interquartile range (IQR) is a measure of statistical dispersion and is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) in a data set. To find the IQR, follow these steps: 1. Order the data set from smallest to largest (which is already done in this case). 2. Divide the data set into quartiles. Q1 is the median of the first half of the data, and Q3 is the median of the second half. 3. Calculate Q1 and Q3, and then find the difference between them. Let's go through the steps with the given data set: 10, 25, 31, 40, 45, 51, 59, 67, 96, 98 There are 10 data points, so we can exactly divide this set into two halves for finding Q1 and Q3: First half (for Q1): 10, 25, 31, 40, 45 Second half (for Q3): 51, 59, 67, 96, 98 Now let's find Q1, the median of the first half: Q1 = 31 (since 31 is the middle value in the first half) And Q3, the median of the second half: Q3 = 67 (since 67 is the middle value in the second half) Finally, calculate the IQR: IQR = Q3 - Q1 IQR = 67 - 31 IQR = 36 So, the interquartile range of the given data set is 36.
Understanding Quartiles and Median
To solve for the lower quartile, median, and upper quartile, we need to understand that these are measures of central tendency and dispersion within a dataset. 1. **Lower quartile (Q1)**: This is the median of the first half of the dataset. Since there are five data points, we divide the dataset into two parts, with the median being the third number. For the first half (2, 6, 6), the lower quartile is the median of these, which is 6. 2. **Median**: This is the middle value of the dataset when it is ordered. Since the dataset (2, 6, 6, 7, 9) is already ordered and has an odd number of data points, the median is the middle number, which is 6. 3. **Upper quartile (Q3)**: This is the median of the second half of the dataset. For the second half (6, 7, 9), the upper quartile is the median of these, which is 7. So, your answers are: Lower quartile (Q1) = 6 Median = 6 Upper quartile (Q3) = 7
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