Complaints

The table is given:
days complaints
0-4 2
5-9 4
10-14 8
15-19 6
20-24 4
25-29 3
30-34 3

1.1 What percentage of complaints were resolved within 2weeks?
1.2 calculate the mean number of days to resolve these complaints.
1.3 calculate the modal number of days to resolve these complaints.
1.4 determine the standard deviation.

Correct answer:

a =  46.6667 %
b =  16.5
c =  12
d =  8.545

Step-by-step explanation:

T=2 7=14 d n=2+4+8+6+4+3+3=30 a=100 2+4+8n=100 2+4+830=1403%=46.6667%
h1=(0+4)/2=2 h2=(5+9)/2=7 h3=(10+14)/2=12 h4=(15+19)/2=17 h5=(20+24)/2=22 h6=(25+29)/2=27 h7=(30+34)/2=32  b=2 h1+4 h2+8 h3+6 h4+4 h5+3 h6+3 h7n=2 2+4 7+8 12+6 17+4 22+3 27+3 3230=332=1612=16.5
c=h3=12
r=2 (h1b)2+4 (h2b)2+8 (h3b)2+6 (h4b)2+4 (h5b)2+3 (h6b)2+3 (h7b)2=2 (216.5)2+4 (716.5)2+8 (1216.5)2+6 (1716.5)2+4 (2216.5)2+3 (2716.5)2+3 (3216.5)2=42352=211712=2117.5  d=rn1=2117.5301=8.545



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Math Teacher
We checked the solution with our statistical calculator:

https://www.hackmath.net/en/calculator/frequency-table?input=0-4+5-9+10-14+15-19+20-24+25-29+30-34%0D%0Af%3A+2+4+8+6+4+3+3

data we enter as grouped frequency table:
0-4 5-9 10-14 15-19 20-24 25-29 30-34
f: 2 4 8 6 4 3 3

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