Question
Find the upper quartile of the given data below:
11
,
8
,
5
,
4
,
7
,
6
,
9
,
10
,
12
11, 8, 5, 4, 7, 6, 9, 10, 12
Answer:
Answers
GPT-4o mini
To find the upper quartile (Q3) of the given data set, we can follow these steps:
1. **Arrange the Data**: First, sort the data in ascending order.
Sorted data: 4, 5, 6, 7, 8, 9, 10, 11, 12
2. **Calculate the Position of Q3**: The upper quartile (Q3) is the median of the upper half of the data. To find its position, we use the formula:
\[
Q3 = \frac{3(n + 1)}{4}
\]
where \( n \) is the number of data points.
In this case, there are 9 data points.
\[
Q3 \text{ position} = \frac{3(9 + 1)}{4} = \frac{30}{4} = 7.5
\]
This means Q3 is located halfway between the 7th and 8th values in the sorted list.
3. **Find Q3**: Now we look at the 7th and 8th values:
- 7th value = 10
- 8th value = 11
To find Q3, we take the average of these two values:
\[
Q3 = \frac{10 + 11}{2} = \frac{21}{2} = 10.5
\]
Therefore, the upper quartile (Q3) of the given data is **10.5**.
1. **Arrange the Data**: First, sort the data in ascending order.
Sorted data: 4, 5, 6, 7, 8, 9, 10, 11, 12
2. **Calculate the Position of Q3**: The upper quartile (Q3) is the median of the upper half of the data. To find its position, we use the formula:
\[
Q3 = \frac{3(n + 1)}{4}
\]
where \( n \) is the number of data points.
In this case, there are 9 data points.
\[
Q3 \text{ position} = \frac{3(9 + 1)}{4} = \frac{30}{4} = 7.5
\]
This means Q3 is located halfway between the 7th and 8th values in the sorted list.
3. **Find Q3**: Now we look at the 7th and 8th values:
- 7th value = 10
- 8th value = 11
To find Q3, we take the average of these two values:
\[
Q3 = \frac{10 + 11}{2} = \frac{21}{2} = 10.5
\]
Therefore, the upper quartile (Q3) of the given data is **10.5**.