How do I find the remaining frequencies? I believe the entire frequency distribution is 2,6,12,12,6,2, for it is a normal distribution, but I am not sure if the middle values can be equivalent. Is this correct? Can someone please explain this to me?
Assume that the first two frequencies are 2 and 6 and ignore the rest of the frequencies. Assuming that it is a normal distribution with 40 sample values, determine the remaining 4 values.
Blood Count Frequency
3.0-4.9 6
5.0-6.9 16
7.0-8.9 9
9.0-10.9 7
11.0-12.9 0
13.0-14.9 2
The Count Frequency is located after each decimal.
Here they are individually: 6,16,9,7,0,2
To find the remaining frequencies, we can start by understanding the distribution and range of the given values.
The provided frequency distribution has seven intervals, each representing a range of values. The frequencies for each interval are given as 2, 6, 12, 12, 6, 2, and unknown values for the remaining intervals. The question states that the distribution is assumed to be normal with 40 sample values.
To determine the remaining frequencies, we can consider the total frequency for the distribution.
The first two frequencies are given as 2 and 6, which sum up to 8. We can subtract this sum from the assumed total frequency of 40 to find the remaining frequency.
Total frequency - Sum of known frequencies = Remaining frequency
40 - 8 = 32
So, there are still 32 remaining frequency values to be distributed among the remaining intervals.
To distribute these frequencies, we need to consider the relative proportions of the known frequencies. Looking at the known frequencies, we can see that they form a symmetric distribution, with the highest frequency occurring for the third interval (12) and then decreasing towards the edge intervals (2).
To maintain this symmetry, we can distribute the remaining frequencies in a similar pattern. Starting from the third interval (7.0-8.9), we can assign a frequency of 12 to keep the distribution symmetric. Then, for the next interval (9.0-10.9), we can assign a frequency proportional to the proportion of the original frequency. In this case, it would be (12/16)*32 = 24.
Following this pattern, we can distribute the remaining frequencies for the remaining intervals as:
11.0-12.9: 0
13.0-14.9: 2
15.0-16.9: 2
17.0-18.9: 6
So, the final distribution with the remaining frequencies would be:
2, 6, 12, 12, 6, 2, 12, 24, 0, 2, 2, 6.
This distribution maintains the original symmetry of the known frequencies while accommodating the additional values.