Record 7 digits (0-9) in ascending order that have an inter-quartile range of 4.
To determine 7 digits (0-9) in ascending order that have an interquartile range of 4, we need to first understand what interquartile range is. The interquartile range is a measure of statistical dispersion, which measures the spread of data values within a dataset.
Now, since we are looking for 7 digits, we will need to determine the first quartile (Q1) and the third quartile (Q3). The difference between Q3 and Q1 will give us the interquartile range.
To find 7 ascending digits with an interquartile range of 4, we need to consider the following steps:
Step 1: Determine the third quartile (Q3)
To find Q3, we divide the total number of observations (in this case, 10 digits from 0-9) by 4 (since we want the third quartile) and multiply it by 3. This gives us the position of the third quartile in the sorted dataset.
10 / 4 * 3 = 7.5
Since 7.5 is not a whole number, we can round it up to 8. This means that the eighth digit in the sorted dataset will be the third quartile (Q3).
Step 2: Determine the first quartile (Q1)
To find Q1, we divide the total number of observations by 4 and multiply it by 1. This gives us the position of the first quartile in the sorted dataset.
10 / 4 * 1 = 2.5
Again, since 2.5 is not a whole number, we can round it up to 3. This means that the third digit in the sorted dataset will be the first quartile (Q1).
Step 3: Calculate the interquartile range (IQR)
The interquartile range (IQR) is the difference between Q3 and Q1. In our case:
IQR = Q3 - Q1 = 8 - 3 = 5
However, we need an interquartile range of 4, so we need to adjust our dataset.
Step 4: Adjust the dataset
Since our calculated IQR is 5, but we need an IQR of 4, we'll need to adjust our dataset accordingly. We can adjust by removing one number from the dataset or adding a fourth quartile (Q4).
In this case, to keep the dataset as 7 digits, we'll choose to remove one number. We'll remove the digit 1 from our dataset.
The resulting 7-digit dataset in ascending order with an interquartile range of 4 is: 0, 2, 3, 4, 5, 6, 9