Find the first and third quartiles, Q1 and Q3, of the following set of numbers.341, 240, 187, 373, 241, 455, 276, 210, 321
I searched Google under the key words "Quartiles" to get these possible sources:
(Broken Link Removed)
http://www.shodor.org/interactivate/discussions/BoxPlot/
http://en.wikipedia.org/wiki/Quartile
http://www.vias.org/tmdatanaleng/cc_quartile.html
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search.
I hope this helps. Thanks for asking.
To find the first and third quartiles (Q1 and Q3) of a set of numbers, you can follow these steps:
1. Start by arranging the numbers in ascending order:
187, 210, 240, 241, 276, 321, 341, 373, 455
2. Next, calculate the position of the median (Q2). In this case, since we have an odd number of data points (9), Q2 will be the middle number. Q2 = 276.
3. Divide the data into two halves:
- Lower half: 187, 210, 240, 241, 276
- Upper half: 321, 341, 373, 455
4. To find Q1, calculate the position of the median of the lower half. Since there are 5 numbers, Q1 will be the value at the (5+1)/4 = 1.5th position. In this case, it falls between the first and second number, so we take the average of these two values: (210 + 240)/2 = 225.
5. Similarly, to find Q3, calculate the position of the median of the upper half. Since there are 4 numbers, Q3 will be the value at the 3(4+1)/4 = 3.75th position. In this case, it falls between the third and fourth number, so we take the average of these two values: (341 + 373)/2 = 357.
Therefore, the first quartile (Q1) is 225 and the third quartile (Q3) is 357 for the given set of numbers.