Please help me to find the first and third quartiles, Q1 and Q3, of the following set of numbers.13, 7, 15, 13, 13, 12, 9, 11, 19, 9

Qrrange the numbers in ascending order, like this:
7, 9, 9, 11, 12, 13, 13, 13, 15, 19
Now divide then into the lowest quartile (Q1), second quartile, third quarter (Q3), and largest quartile.

Since there are ten numbers, there will be 2 1/2 numbers per quartile. The third largest number (9), be part of both Q1 and Q2, for example.
The third quartile will be the number 13 only.

The first quartile Q1 (or lowest quartile) is the median (middle) of the lowest half of the numbers. The third quartile Q3 is the median (middle) of the upper half of the numbers. First order the numbers from lowest to highest:
7, 9, 9, 11, 12, 13, 13, 13, 15, 19

The median of this data set is the middle value of all the numbers. The middle is between 12 and 13 (for an even set of numbers), which would be 12.5 in this case. (For an even set of numbers, you take the average of the two middle numbers. For an odd set of numbers, the median is the middle number.)

Pick the middle number of the five lowest numbers for Q1. Pick the middle of the 5 highest numbers for Q3.

Hopefully, this will help with other problems of this type.

36

To find the first quartile (Q1), we need to find the median of the lowest half of the numbers.

The lowest half of the numbers is: 7, 9, 9, 11, 12

To find the median, we have to find the middle number in this set. Since there are 5 numbers, the middle number is the third number, which is 9.

Therefore, the first quartile (Q1) is 9.

To find the third quartile (Q3), we need to find the median of the upper half of the numbers.

The upper half of the numbers is: 13, 13, 13, 15, 19

To find the median, we have to find the middle number in this set. Since there are 5 numbers, the middle number is the third number, which is 13.

Therefore, the third quartile (Q3) is 13.

To find the first and third quartiles (Q1 and Q3) of a set of numbers, follow these steps:

1. Arrange the numbers in ascending order.
2. Determine the median (middle value) of the entire set of numbers.
- If the set has an odd number of values, the median is the middle number.
- If the set has an even number of values, the median is the average of the two middle numbers.
3. Divide the numbers into two halves: the lower half and the upper half.
4. Find the median of the lower half to determine Q1.
- For an odd number of values, this will be the middle number of the lower half.
- For an even number of values, take the average of the two middle numbers of the lower half.
5. Find the median of the upper half to determine Q3.
- For an odd number of values, this will be the middle number of the upper half.
- For an even number of values, take the average of the two middle numbers of the upper half.

In the example you provided (13, 7, 15, 13, 13, 12, 9, 11, 19, 9), the numbers arranged in ascending order are 7, 9, 9, 11, 12, 13, 13, 13, 15, 19.

The median of this set is the middle value, which is between 12 and 13 for an even set. Therefore, the median is 12.5.

To find Q1, you need to determine the median of the lower half (7, 9, 9, 11, 12). Since there are five values, the middle number is the third value, which is 9.

To find Q3, you need to determine the median of the upper half (13, 13, 13, 15, 19). Since there are five values, the middle number is the third value, which is 13.

So, Q1 is 9 and Q3 is 13.