Solved on Jan 17, 2024
Find the five-number summary for the gold, silver, and bronze medals won by 19 countries at the 2012 London Olympics: (gold), (silver), and (bronze).
STEP 1
Assumptions
1. The data provided represents the number of each type of medal won by the 19 countries.
2. The five-number summary includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum.
3. The data for each type of medal is already sorted in ascending order.
STEP 2
Identify the minimum value for each type of medal, which is the first number in each sorted list.
Gold minimum:
Silver minimum:
Bronze minimum:
STEP 3
Identify the maximum value for each type of medal, which is the last number in each sorted list.
Gold maximum:
Silver maximum:
Bronze maximum:
STEP 4
Calculate the median (the middle value) for each type of medal. Since there are 19 countries, the median will be the value at position .
Gold median:
Silver median:
Bronze median:
STEP 5
To find the first quartile (Q1), we need to find the median of the first half of the data. For 19 data points, the first half is the first 9 numbers. The median of these 9 numbers is the value at position .
Gold Q1:
Silver Q1:
Bronze Q1:
STEP 6
To find the third quartile (Q3), we need to find the median of the second half of the data. For 19 data points, the second half is the last 9 numbers. The median of these 9 numbers is the value at position , counting from the median to the end of the list.
Gold Q3:
Silver Q3:
Bronze Q3:
STEP 7
List the five-number summary for each type of medal.
Gold:
- Minimum:
- Q1:
- Median:
- Q3:
- Maximum:
Silver:
- Minimum:
- Q1:
- Median:
- Q3:
- Maximum:
Bronze:
- Minimum:
- Q1:
- Median:
- Q3:
- Maximum:
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