Find the five-number summary of the following set of numbers:
349, 243, 119, 363, 246, 505, 263, 221, 324
Arrange the scores in order of value to find the five-number summary (max, min, median, first and third quartiles).
I'll let you do the calculations.
To find the five-number summary of a data set, you need to calculate the minimum value (min), the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value (max). Here's how you can do it step by step for the given set of numbers:
Step 1: Arrange the numbers in ascending order:
119, 221, 243, 246, 263, 324, 349, 363, 505
Step 2: Find the minimum value (min), which is the smallest number in the set:
min = 119
Step 3: Find the first quartile (Q1). Q1 is the median of the lower half of the data set. To find Q1, split the data set into two halves. Since the data set has 9 numbers, the lower half has (9 + 1) / 2 = 5 numbers.
Lower half: 119, 221, 243, 246, 263
Q1 = median of the lower half = (243 + 246) / 2 = 244.5
Step 4: Find the median (Q2), which is the middle value of the data set. Since the data set has an odd number of values (9), Q2 is the 5th value:
Q2 = 263
Step 5: Find the third quartile (Q3). Q3 is the median of the upper half of the data set. To find Q3, split the data set into two halves. The upper half has the same number of values as the lower half.
Upper half: 324, 349, 363, 505
Q3 = median of the upper half = (349 + 363) / 2 = 356
Step 6: Find the maximum value (max), which is the largest number in the set:
max = 505
So, the five-number summary of the given set of numbers is:
Min: 119
Q1: 244.5
Q2: 263
Q3: 356
Max: 505