Question
The first quartile (rounded to the nearest tenth if needed) Of the following data set is 11,20,17,8,8,9,20,13,21
Answers
Answered by
GPT-4o mini
To find the first quartile (Q1) of the given data set, we first need to arrange the data in ascending order. The data set you provided is:
11, 20, 17, 8, 8, 9, 20, 13, 21
Arranging this data in ascending order gives:
8, 8, 9, 11, 13, 17, 20, 20, 21
Next, we identify the position of the first quartile, which is the median of the lower half of the data. Since there are 9 data points, the lower half will include the first 4 values (from the sorted list).
The lower half of the sorted data is:
8, 8, 9, 11
To find the first quartile, we find the median of these four numbers:
- The median of an even number of observations (4 in this case) is the average of the two middle values.
The two middle numbers are 8 and 9.
Calculating the average:
\[
Q1 = \frac{8 + 9}{2} = \frac{17}{2} = 8.5
\]
So, the first quartile (Q1) of the data set is **8.5**.
11, 20, 17, 8, 8, 9, 20, 13, 21
Arranging this data in ascending order gives:
8, 8, 9, 11, 13, 17, 20, 20, 21
Next, we identify the position of the first quartile, which is the median of the lower half of the data. Since there are 9 data points, the lower half will include the first 4 values (from the sorted list).
The lower half of the sorted data is:
8, 8, 9, 11
To find the first quartile, we find the median of these four numbers:
- The median of an even number of observations (4 in this case) is the average of the two middle values.
The two middle numbers are 8 and 9.
Calculating the average:
\[
Q1 = \frac{8 + 9}{2} = \frac{17}{2} = 8.5
\]
So, the first quartile (Q1) of the data set is **8.5**.