Respuesta :
Answer:
a. Class width=4
b.
Class midpoints
46.5
50.5
54.5
58.5
62.5
66.5
70.5
c.
Class boundaries
44.5-48.5
48.5-52.5
52.5-56.5
57.5-60.5
60.5-64.5
64.5-68.5
68.5-72.5
Step-by-step explanation:
There are total 7 classes in the given frequency distribution. By arranging the frequency distribution into the refine form we get,
Class
Interval frequency
45-48 1
49-52 3
53-56 5
57-60 11
61-64 7
65-68 7
69-72 1
a)
Class width is calculated by taking difference of consecutive two upper class limits or two lower class limits.
Class width=49-45=4
b)
The midpoints of each class is calculated by taking average of upper class limit and lower class limit for each class.
[tex]M=\frac{lower class limit+upper class limit}{2}[/tex]
Class
Interval Midpoints
45-48 [tex]\frac{45+48}{2}=46.5[/tex]
49-52 [tex]\frac{49+52}{2}=50.5[/tex]
53-56 [tex]\frac{53+56}{2}=54.5[/tex]
57-60 [tex]\frac{57+60}{2}=58.5[/tex]
61-64 [tex]\frac{61+64}{2}=62.5[/tex]
65-68 [tex]\frac{65+68}{2}=66.5[/tex]
69-72 [tex]\frac{69+72}{2}=70.5[/tex]
c)
Class boundaries are calculated by subtracting 0.5 from the lower class limit and adding 0.5 to the upper class interval.
Class
Interval Class boundary
45-48 44.5-48.5
49-52 48.5-52.5
53-56 52.5-56.5
57-60 56.5-60.5
61-64 60.5-64.5
65-68 64.5-68.5
69-72 68.5-72.5
The required values are
a. 4
b.
[tex]\dfrac{45 + 48}{2} = 46.5\\\dfrac{61+64}{2} = 62.5\\\dfrac{49+52}{2} = 50.5\\\dfrac{65+68}{2} = 66.5\\\dfrac{53+56}{2} = 54.5\\\dfrac{69+72}{2} = 70.5\\\dfrac{57+60}{2} = 68.5[/tex]
c. 45-48 to 44.5-48.5
61-64 to 60.5-64.5
49-52 to 48.5-52.5
65-68 to 64.5-68.5
53-56 to 52.5-56.5
69-72 to 68.5-72.5
57-60 to 56.5-60.5
Frequency distribution
A function showing the number of instances in which a variable takes each of its possible values.
Given
Data set frequency
How to calculate the class width, mid point, and boundaries?
a. Class width is evaluated by taking the difference of consecutive of two upper class or two lower class limits.
Class width = 49 - 45
Class width = 4
b. Average of upper class limit and lower class limit for each class.
[tex]\dfrac{45 + 48}{2} = 46.5\\\dfrac{61+64}{2} = 62.5\\\dfrac{49+52}{2} = 50.5\\\dfrac{65+68}{2} = 66.5\\\dfrac{53+56}{2} = 54.5\\\dfrac{69+72}{2} = 70.5\\\dfrac{57+60}{2} = 68.5[/tex]
c. It is calculated by subtracting 0.5 from the lower limit and adding to the upper limit.
45-48 to 44.5-48.5
61-64 to 60.5-64.5
49-52 to 48.5-52.5
65-68 to 64.5-68.5
53-56 to 52.5-56.5
69-72 to 68.5-72.5
57-60 to 56.5-60.5
Thus this is the required values.
More about the frequency distribution link is given below.
https://brainly.com/question/24973035
