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Find Q2

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Find Q2


1. **State the problem:** We are given a list of daily expenses and asked to find the second quartile (Q2), which is the median of the data. 2. **Recall the formula and rules:** - The second quartile (Q2) is the median, which divides the data into two equal halves. - To find the median, first sort the data in ascending order. - If the number of data points $n$ is odd, median is the middle value at position $\frac{n+1}{2}$. - If $n$ is even, median is the average of the two middle values at positions $\frac{n}{2}$ and $\frac{n}{2}+1$. 3. **Sort the data:** $[153, 156, 176, 178, 181, 182, 194, 206, 232, 233, 236, 243, 257, 262, 270, 272, 275, 281, 298, 305, 311, 317, 348, 347, 366, 369, 418, 422, 434, 447, 449, 457, 462, 475, 482, 484, 490]$ 4. **Count the data points:** There are $n=37$ data points (odd). 5. **Find the median position:** $$\frac{n+1}{2} = \frac{37+1}{2} = 19$$ 6. **Find the median value:** The 19th value in the sorted list is $298$. 7. **Conclusion:** The second quartile (Q2) or median of the daily expenses is **298**.