Below are the lengths (in minutes) of 12 phone calls made on an 800 line to a business on one day. Find the five number summary for this data.
14,6, 12, 19, 2, 35, 5, 4, 3, 7, 5, 8
To find the five number summary for this data, we need to identify the minimum value, maximum value, median, and the first and third quartiles.
1. Sort the data in ascending order: 2, 3, 4, 5, 5, 6, 7, 8, 12, 14, 19, 35.
2. Find the minimum value: The minimum value is 2.
3. Find the maximum value: The maximum value is 35.
4. Calculate the median: The median is the middle value of the sorted data. In this case, there are 12 data points, so the median is located halfway between the 6th and 7th values. The 6th value is 6, and the 7th value is 7. So, the median is (6+7)/2 = 6.5.
5. Calculate the first quartile (Q1): The first quartile is the median of the lower half of the data set. In this case, we need to consider the 6 data points below the median. The median of these 6 values can be found in the same way as step 4. The 3rd value is 4, and the 4th value is 5. So, the first quartile is (4+5)/2 = 4.5.
6. Calculate the third quartile (Q3): The third quartile is the median of the upper half of the data set. In this case, we need to consider the 6 data points above the median. The median of these 6 values can be found in the same way as step 4. The 9th value is 12, and the 10th value is 14. So, the third quartile is (12+14)/2 = 13.
Therefore, the five number summary for this data is:
Minimum: 2
First quartile (Q1): 4.5
Median: 6.5
Third quartile (Q3): 13
Maximum: 35
To find the five number summary for the given data, we need to calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.
Step 1: Sort the data in ascending order:
2, 3, 4, 5, 5, 6, 7, 8, 12, 14, 19, 35
Step 2: Calculate the minimum and maximum values:
Minimum: 2
Maximum: 35
Step 3: Calculate the median (Q2):
The median is the middle value of the sorted data:
Median (Q2): 6
Step 4: Calculate the first quartile (Q1):
The first quartile is the median of the lower half of the data.
Lower half of the data: 2, 3, 4, 5, 5
Median of lower half: 4
First quartile (Q1): 4
Step 5: Calculate the third quartile (Q3):
The third quartile is the median of the upper half of the data.
Upper half of the data: 7, 8, 12, 14, 19, 35
Median of upper half: 12
Third quartile (Q3): 12
The five-number summary for the given data is:
Minimum: 2
First Quartile (Q1): 4
Median (Q2): 6
Third Quartile (Q3): 12
Maximum: 35