Question
A random sample of bonuses (in millions of dollars) paid by large companies to their executives is shown below.
Class boundary
Frequency
0.5----3.5
11
3.5----6.5
12
6.5----9.5
4
9.5----12.5
2
12.5---15.5
1
Find
P25
Class boundary
Frequency
0.5----3.5
11
3.5----6.5
12
6.5----9.5
4
9.5----12.5
2
12.5---15.5
1
Find
P25
Answers
There are no human answers yet.
Answered by
GPT 3.5
To find P25 (the 25th percentile), we need to find the value that separates the lowest 25% of the data from the rest of the data.
First, we calculate the total number of observations:
11 + 12 + 4 + 2 + 1 = 30
Next, we calculate the position of the 25th percentile in the data set:
25/100 * 30 = 7.5
Since the position is not an integer, we need to take the average of the 7th and 8th values in the data set.
Since 7 is in the 0.5-3.5 class, and the boundaries for this class are 0.5 and 3.5, we can calculate the width of this class:
3.5 - 0.5 = 3
To find the value at the 25th percentile, we can use the formula:
P25 = lower boundary of the class + [(position - cumulative frequency of the class before) / frequency of the class] * width of the class
P25 = 0.5 + [(7.5 - 0) / 11] * 3
P25 = 0.5 + (7.5/11) * 3
P25 = 0.5 + 0.6818181818181818 * 3
P25 = 0.5 + 2.0454545454545454
P25 ≈ 2.545
Therefore, the 25th percentile of the data set is approximately 2.545 million dollars.
First, we calculate the total number of observations:
11 + 12 + 4 + 2 + 1 = 30
Next, we calculate the position of the 25th percentile in the data set:
25/100 * 30 = 7.5
Since the position is not an integer, we need to take the average of the 7th and 8th values in the data set.
Since 7 is in the 0.5-3.5 class, and the boundaries for this class are 0.5 and 3.5, we can calculate the width of this class:
3.5 - 0.5 = 3
To find the value at the 25th percentile, we can use the formula:
P25 = lower boundary of the class + [(position - cumulative frequency of the class before) / frequency of the class] * width of the class
P25 = 0.5 + [(7.5 - 0) / 11] * 3
P25 = 0.5 + (7.5/11) * 3
P25 = 0.5 + 0.6818181818181818 * 3
P25 = 0.5 + 2.0454545454545454
P25 ≈ 2.545
Therefore, the 25th percentile of the data set is approximately 2.545 million dollars.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.