The data below represents the amount of grams of carbohydrates in a sample serving of breakfast cereal.
10
18
24
30
19
22
24
20
18
25
20
22
19What is the interquartile range (midspread) for this data?
Arrange in order of value. It would range from the 4th ranked to the tenth.
To find the interquartile range (IQR), you first need to find the lower quartile (Q1) and the upper quartile (Q3).
Step 1: Arrange the data in ascending order:
10, 18, 18, 19, 19, 20, 20, 22, 22, 24, 24, 25, 30
Step 2: Find the median (Q2), which is the middle value of the data:
Q2 = 20
Step 3: Find Q1, which is the median of the lower half of the data:
Q1 = median of (10, 18, 18, 19, 19, 20) = 18
Step 4: Find Q3, which is the median of the upper half of the data:
Q3 = median of (22, 22, 24, 24, 25, 30) = 23
Step 5: Calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 23 - 18 = 5
The interquartile range (midspread) for this data is 5 grams.
To calculate the interquartile range (IQR), you need to first find the first quartile (Q1) and the third quartile (Q3) of the data set.
Here's how you can calculate the interquartile range for the given data:
1. Sort the data in ascending order:
10, 18, 18, 19, 19, 20, 20, 22, 22, 24, 24, 25, 30
2. To find the first quartile (Q1), you need to find the median of the lower half of the data set. In this case, the lower half starts from the first value (10) and ends at the median (20). The median of the lower half is the value halfway between the two middle terms, which are 10 and 19. So, Q1 = (10 + 19) / 2 = 14.5.
3. To find the third quartile (Q3), you need to find the median of the upper half of the data set. In this case, the upper half starts from the median (20) and ends at the last value (30). The median of the upper half is the value halfway between the two middle terms, which are 22 and 24. So, Q3 = (22 + 24) / 2 = 23.
4. Finally, you can calculate the interquartile range (IQR) by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 23 - 14.5 = 8.5.
Therefore, the interquartile range (midspread) for this data is 8.5 grams.