Find the five-number summary of the following set of numbers.
335, 233, 185, 392, 235, 518, 281, 208, 318
First, arrange the set of numbers in order, with the lowest first.
185, 208, 233, 235, 281, 318, 335, 392, 518
Then, follow the instructions in this website.
http://illuminations.nctm.org/Lessons/States/FiveNumSum.htm
We'll be glad to check your answers.
Here is a definition of Five-number summary:
(1) the minimum (smallest observation)
(2) the lower quartile or first quartile (which cuts off the lowest 25% of the data)
(3) the median (middle value)
the upper quartile or third quartile (4) (which cuts off the highest 25% of the data)
(5) the maximum (largest observation)
In your case the median is 281 , the minimum is 185 and the maximum is 518. For the two quartiles, take the third and seventh largest numbers of the group.
293.55
To find the five-number summary of a set of numbers, we need to calculate the minimum, first quartile, median, third quartile, and maximum. Here's how to get each of these values:
1. Minimum: The minimum value is the smallest value in the set. In this case, the minimum is 185.
2. First Quartile (Q1): The first quartile is the median of the lower half of the dataset. To find Q1, first, arrange the numbers in ascending order: 185, 208, 233, 235, 281, 318, 335, 392, 518. Since we have 9 numbers, the middle number of the lower half is the 5th number (n/2). So Q1 is 233.
3. Median (Q2): The median is the middle value of the dataset. Again, arrange the numbers in ascending order: 185, 208, 233, 235, 281, 318, 335, 392, 518. Since we have 9 numbers, the middle value is the 5th number (n/2). So Q2 (median) is also 233.
4. Third Quartile (Q3): The third quartile is the median of the upper half of the dataset. Arrange the numbers in ascending order: 185, 208, 233, 235, 281, 318, 335, 392, 518. Since we have 9 numbers, the middle number of the upper half is the 5th number (n/2). So Q3 is 335.
5. Maximum: The maximum value is the largest value in the set. In this case, the maximum is 518.
Therefore, the five-number summary of the given set of numbers is:
Minimum: 185
First Quartile (Q1): 233
Median (Q2): 233
Third Quartile (Q3): 335
Maximum: 518