2005 2006 2007 2008
Plant 1 20 4 25 10
Plant 2 25 5 5 48
Plant 3 20 8 20 32
Plant 4 43 10 10 47
Plant 5 40 11 15 48
A gardener recorded how many tomatoes 5 plants produced each year. Which year had the LARGEST interquartile range of tomatoes produced?
A)
2005
B)
2006
C)
2007
D)
2008
Think it's 2005
To find the year with the largest interquartile range of tomatoes produced, we first need to find the interquartile range for each year.
The interquartile range is calculated by finding the difference between the upper quartile (Q3) and the lower quartile (Q1).
To find Q1 and Q3, we need to calculate the median (Q2) and the median of the lower half (Q1) and the upper half (Q3) of the data.
Let's calculate the interquartile range for each year:
For 2005:
Q1 = median of {20, 4} = (4 + 20) / 2 = 12
Q3 = median of {25, 10} = (10 + 25) / 2 = 17.5
Interquartile Range = Q3 - Q1 = 17.5 - 12 = 5.5
For 2006:
Q1 = median of {25, 5} = (5 + 25) / 2 = 15
Q3 = median of {5, 48} = (5 + 48) / 2 = 26.5
Interquartile Range = Q3 - Q1 = 26.5 - 15 = 11.5
For 2007:
Q1 = median of {20, 8} = (8 + 20) / 2 = 14
Q3 = median of {20, 32} = (20 + 32) / 2 = 26
Interquartile Range = Q3 - Q1 = 26 - 14 = 12
For 2008:
Q1 = median of {43, 10} = (10 + 43) / 2 = 26.5
Q3 = median of {10, 47} = (10 + 47) / 2 = 28.5
Interquartile Range = Q3 - Q1 = 28.5 - 26.5 = 2
Based on these calculations, the largest interquartile range of tomatoes produced is in:
C) 2007.
To find the year with the largest interquartile range of tomatoes produced, we need to calculate the interquartile range (IQR) for each year and compare them.
Step 1: Calculate the 1st quartile (Q1) and 3rd quartile (Q3) for each year.
To do this, we need to organize the data for each year in ascending order:
For 2005:
20, 25, 20, 43, 40
Organized in ascending order: 20, 20, 25, 40, 43
Q1 = median of the lower half: Q1 = (20 + 20) / 2 = 20
Q3 = median of the upper half: Q3 = (40 + 43) / 2 = 41.5
For 2006:
4, 5, 8, 10, 11
Organized in ascending order: 4, 5, 8, 10, 11
Q1 = median of the lower half: Q1 = (4 + 5) / 2 = 4.5
Q3 = median of the upper half: Q3 = (10 + 11) / 2 = 10.5
For 2007:
25, 5, 20, 10, 15
Organized in ascending order: 5, 10, 15, 20, 25
Q1 = median of the lower half: Q1 = (5 + 10) / 2 = 7.5
Q3 = median of the upper half: Q3 = (20 + 25) / 2 = 22.5
For 2008:
10, 48, 32, 47, 48
Organized in ascending order: 10, 32, 47, 48, 48
Q1 = median of the lower half: Q1 = (10 + 32) / 2 = 21
Q3 = median of the upper half: Q3 = (48 + 48) / 2 = 48
Step 2: Calculate the interquartile range (IQR) for each year.
IQR = Q3 - Q1
For 2005: IQR = 41.5 - 20 = 21.5
For 2006: IQR = 10.5 - 4.5 = 6
For 2007: IQR = 22.5 - 7.5 = 15
For 2008: IQR = 48 - 21 = 27
Step 3: Compare the IQR values to find the year with the largest IQR.
2005: IQR = 21.5
2006: IQR = 6
2007: IQR = 15
2008: IQR = 27
The year with the largest IQR is 2008 (D), with an IQR of 27.