Question

Identify the class​ width, class​ midpoints, and class boundaries for the given frequency distribution.

Answer 1

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.

$M=\frac{lower class limit+upper class limit}{2}$

Class

Interval Midpoints

45-48 $\frac{45+48}{2}=46.5$

49-52 $\frac{49+52}{2}=50.5$

53-56 $\frac{53+56}{2}=54.5$

57-60 $\frac{57+60}{2}=58.5$

61-64 $\frac{61+64}{2}=62.5$

65-68 $\frac{65+68}{2}=66.5$

69-72 $\frac{69+72}{2}=70.5$

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