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?
1. Place the data in ascending order.
2. Group the data into two equal parts. You have an odd number of pieces of data, so put brackets around the first six numbers, leave the middle number on its own, and put brackets around the last six numbers.
3. Find the median of the first group of numbers. This is called Q1.
4. Find the median of the second group of numbers. This is called Q3.
5. Q3 - Q1 is the interquartile range.
To find the interquartile range (IQR), you need to calculate the values for the first quartile (Q1) and the third quartile (Q3) of the data.
1. Begin by organizing the data in ascending order:
10, 18, 18, 19, 19, 20, 20, 22, 22, 24, 24, 25, 30
2. Find the median (Q2), which is the middle value of the data set. In this case, there are 13 data points, so the median is the 7th value:
Median (Q2) = 20
3. Next, find the median of the lower half of the data, which is the first quartile (Q1). In this case, the lower half consists of:
10, 18, 18, 19, 19, 20
Since there are 6 data points, the middle value is the average of the 3rd and 4th values:
Q1 = (18 + 19) / 2 = 18.5
4. Finally, find the median of the upper half of the data, which is the third quartile (Q3). In this case, the upper half consists of:
22, 22, 24, 24, 25, 30
Again, there are 6 data points, so the middle value is the average of the 3rd and 4th values:
Q3 = (24 + 25) / 2 = 24.5
The interquartile range (IQR) is calculated by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 24.5 - 18.5 = 6
Therefore, the interquartile range (midspread) for this data set is 6 grams.