find the five-number summary of the following set of numbers, 349,243,119,363,246,505,263,221,324
To find the five-number summary of a set of numbers, you need to determine the minimum, first quartile (Q1), median (Q2 or the second quartile), third quartile (Q3), and maximum values.
Here are the steps to find the five-number summary of the given set of numbers:
Step 1: Arrange the set of numbers in ascending order:
119, 221, 243, 246, 263, 324, 349, 363, 505
Step 2: Find the minimum value, which is the smallest number in the set:
Minimum = 119
Step 3: Find the maximum value, which is the largest number in the set:
Maximum = 505
Step 4: Find the median (Q2), which is the middle value of the set. If there is an odd number of data points, the median is the middle number. If there is an even number of data points, the median is the average of the two middle numbers.
Median = (246 + 263) / 2 = 254.5
Step 5: Find the first quartile (Q1), which is the median of the lower half of the data set. It is the value below which 25% of the data falls.
Q1 = (221 + 243) / 2 = 232
Step 6: Find the third quartile (Q3), which is the median of the upper half of the data set. It is the value below which 75% of the data falls.
Q3 = (349 + 363) / 2 = 356
The five-number summary for the given set of numbers is:
Minimum = 119
Q1 = 232
Median = 254.5
Q3 = 356
Maximum = 505