Answer:
Less than 30: 26
Less than 40: 62
Less than 50: 75
Less than 60: 78
Less than 70: 85
Less than 80: 86
Less than 90: 88
Step-by-step explanation:
We have this frequency information:
20-29: 26
30-39: 36
40-49: 13
50-59: 3
60-69: 7
70-79: 1
80-89: 2
We can add each category and have a cumulative frequency table
<30: 26
<40: 26+36 = 62
<50: 62 +13 = 75
<60: 75 + 3 = 78
<70: 78 + 7 = 85
<80: 85 + 1 = 86
<90: 86 + 2 = 88
The required cumulative frequency distribution table is
Given,
The cumulative frequency of the first class, that is, less than 30 will be [tex]f_1=27[/tex]
The cumulative frequency of the third class, that is, less than 50 will be calculated as:
[tex]f_1+f_2+f_3=27+23+11=75[/tex]
The cumulative frequency of the fourth class, that is, less than 60 will be calculated as:
[tex]f_1+f_2+f_3+f_4=27+23+11+3=78[/tex]
The cumulative frequency of the fifth class, that is, less than 70 will be calculated as:
[tex]f_1+f_2+f_3+f_4+f_5=27+23+11+3+5=83[/tex]
The cumulative frequency of the sixth class, that is, less than 80 will be calculated as:
[tex]f_1+f_2+f_3+f_4+f_5+f_6=27+23+11+3+5+1=84[/tex]
The cumulative frequency of the seventh class, that is, less than 90 will be calculated as:
[tex]f_1+f_2+f_3+f_4+f_5+f_6+f_7=27+23+11+3+5+1+2=86[/tex]
The obtained cumulative frequency distribution is attached below:
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