A baker measured the length of different loaves of bread. The interquartile range of a data set was 12 inches. Which statement is also true for the data set?
Interquartile range = middle 50%. Therefore you are speaking of mean (9) ± 3. What proportion are greater than 12 or less than 6?
To determine which statement is true for the data set, it would be helpful to understand what the interquartile range is. The interquartile range (IQR) is a measure of the spread or dispersion of a dataset. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
Here's how you can find the IQR for the given data set:
1. Arrange the data set in ascending order.
2. Find the median of the entire data set, which is the second quartile (Q2) and separates the data into two equal halves.
3. Find the median of the lower half of the data set, which is the first quartile (Q1).
4. Find the median of the upper half of the data set, which is the third quartile (Q3).
5. Calculate the IQR by subtracting Q1 from Q3.
Now, you mentioned that the interquartile range (IQR) of the data set is 12 inches. Based on this information, there are a couple of statements that could be true for the data set:
1. The difference between the third quartile (Q3) and the first quartile (Q1) is 12 inches.
2. The spread of the data set, as measured by the range between the 25th percentile(Q1) and the 75th percentile (Q3), is 12 inches.
3. At least 50% of the data lies within a range of 12 inches.
Therefore, any of the above statements could be true for the data set with an interquartile range of 12 inches. The specific statement would depend on the context and additional information about the data.