If Q2 = D5 = Median
Which means if the 2nd quartile equals to 5th decile and also the median.. then how do we find out the fourth decile?
I mean is there a way to find it out through this?
Then what is D4 going to be?
I am talking about Deciles here..
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion (.4000) and its Z score. Of course, since it is below the mean, it will be negative.
Ah, deciles! The more we divide things, the more fun it gets, doesn't it? Alright, let's see if we can tickle our way to finding D4.
If Q2 (the 2nd quartile) is equal to D5 (the 5th decile), and they are both the median, we know that half of the data falls below this point. So, first things first, let's find the value at Q2/D5.
Now, to find the 4th decile (D4), we know that it covers 40% of the data. So, if we break that down, we can approximate it to the value halfway between D3 (30%) and D5 (50%). Let's call that value "WigglyD4."
Now, if Q2 (the second quartile, which is also the median) is equal to D5 (the 5th decile), it means that "WigglyD4" must also be equal to the median. Therefore, the value at D4 has to be in between the value of D3 and "WigglyD4."
By juggling around these values, we can find the approximate value at D4. However, please note that this is an estimation and might not be completely accurate. But hey, who said decimals didn't have a little wiggle room?
To find the fourth decile (D4), we can use the fact that the second quartile (Q2) is equal to the fifth decile (D5) and also the median.
Since the median represents the middle value of a dataset, and the second quartile represents the value separating the lower 50% from the upper 50% of the dataset, we can conclude that the fourth decile lies between the second quartile and the median.
Therefore, the fourth decile (D4) will be greater than the second quartile (Q2) and less than the median. However, without knowing the actual values of Q2 and the median, it is not possible to determine the exact value of D4 based solely on the given information.
To find the 4th decile (D4) in this scenario, where Q2 = D5 = median, you can use the following steps:
Step 1: Understand the concept of deciles:
Deciles divide a dataset into 10 equal parts. For example, D1 represents the first decile, separating the lowest 10% of the data, while D10 represents the highest 10% of the data.
Step 2: Recognize the properties of the median:
The median divides the data into two equal parts, meaning that 50% of the data points are below the median, and 50% are above it. In other words, the median corresponds to the 5th decile (D5) because it divides the dataset into 50% below and 50% above it.
Step 3: Determine the value of the fourth decile (D4):
Since the midpoint between the 3rd decile (D3) and the 5th decile (D5) corresponds to the median, and D5 is already known to be the median, then the value of D4 can be inferred as the midpoint between D3 and D5.
For example, if the data set is: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.
Step 4: Calculate D3 and D4:
To calculate D3, we need to find the value that separates the lowest 30% of the data points from the remaining 70%. 30% of 10 data points is 0.3 * 10 = 3. Thus, D3 falls between the 3rd and 4th values, which are 5 and 7. Therefore, D3 corresponds to the value 6.
To calculate D4, we need to find the midpoint between the values at the 3rd and 5th deciles (D3 and D5), which are 6 and 11. The midpoint between 6 and 11 is (6 + 11) / 2 = 17 / 2 = 8.5. Hence, D4 is 8.5.
In summary, if Q2 = D5 = median, the 4th decile (D4) can be found by determining the midpoint between the 3rd decile (D3) and the 5th decile (D5).