Heres the problem find the first and third quartiles of the following set of numbers I put them in order 146,218,242,249,277,319,347,391,567 my answer is q1=230 and q3 =369 is this correct

If you used the following formula to calculate the quartiles, the answers are correct.

There are different ways to calculate quartiles. One that is widely used is to calculate the location of the sorted list, given by:
i=(1/4)*(n+1) where n is the number of observations.
According to the formula, n=9, so the quartiles are at locations 2.5 and 7.5, the values of which are obtained by interpolation.

To find the first and third quartiles of a given set of numbers, you need to follow these steps:

Step 1: Put the numbers in ascending order

The set of numbers you provided, in ascending order, is: 146, 218, 242, 249, 277, 319, 347, 391, 567.

Step 2: Calculate the position of the first quartile (Q1)
The formula to calculate the position of the first quartile is (n + 1) / 4, where n represents the total number of observations in your set. In this case, there are 9 numbers, so n = 9.

Using the formula, (9 + 1) / 4 = 10 / 4 = 2.5.
Since the position is not a whole number, you need to find the average of the numbers in positions 2 and 3. The second smallest number is 218, and the third smallest number is 242.

Average of 218 and 242 = (218 + 242) / 2 = 460 / 2 = 230.

Therefore, the first quartile (Q1) is 230.

Step 3: Calculate the position of the third quartile (Q3)
The formula to calculate the position of the third quartile is (3 * (n + 1)) / 4.

Using the formula, (3 * (9 + 1)) / 4 = (3 * 10) / 4 = 30 / 4 = 7.5.
Since the position is not a whole number, you need to find the average of the numbers in positions 7 and 8. The seventh smallest number is 347, and the eighth smallest number is 391.

Average of 347 and 391 = (347 + 391) / 2 = 738 / 2 = 369.

Therefore, the third quartile (Q3) is 369.

Based on the calculations, your answer is correct. The first quartile is 230, and the third quartile is 369.