Answer:
Check it below
Step-by-step explanation:
1) Ordering it we have:
34 38 39 40 44 45 50 51 55 57 58 59 62 63 65 65 67 72 74 78
a) Then let's calculate the First Quartile by calculating the Median
[tex]N=20 \:then\: Md=10th+11st \Rightarrow Md=\frac{57+58}{2}= 57.5[/tex]
Place the Median inside this row of values
34 38 39 40 44 45 50 51 55 57 57.5 58 59 62 63 65 65 67 72 74 78
Calculate the Median of the 10 salaries below the Median, to have the lower Quartile, i.e. <57.5
34 38 39 40 44 45 50 51 55 57
[tex]Q_{1}=\frac{44+45}{2} =44.5[/tex]
Do the Same with the values above 57.5, i.e. >57.5:
58 59 62 63 65 65 67 72 74 78
[tex]Q_{3}=\frac{65+65}{2}=65[/tex]
The Interquartile Range is the difference between the Upper and the Lower Quartile, so
[tex]Q_{3}-Q_{1}=65-44.5=20.5[/tex]
b) The Value of the 30th percentile, is 0.3*N, so 0.3*(20)=6th position
6th position = 45
c) To find that let's set a table with this data, and check the Cumulative Frequency column. (Check the graph below)
The Salary of $62,000 is on the 65% percentile rank, only 35% of the annual salaries are greater than $62,000
