Question

69 randomly selected students were asked the number of pairs of shoes they have. Let X...

69 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:

 # of Pairs of Shoes Frequency 4 5 6 7 8 9 10 11 12 13 6 6 6 10 5 6 8 7 5 10

The mean is:

The median is:

The sample standard deviation is:

The first quartile is:

The third quartile is:

What percent of the respondents have at least 13 pairs of Shoes? % :

18% of all respondents have fewer than how many pairs of Shoes?:

 x f f*M f*M2 cf cf% 4 6 24 96 6 8.7% 5 6 30 150 12 17.4% 6 6 36 216 18 26.1% 7 10 70 490 28 40.6% 8 5 40 320 33 47.8% 9 6 54 486 39 56.5% 10 8 80 800 47 68.1% 11 7 77 847 54 78.3% 12 5 60 720 59 85.5% 13 10 130 1690 69 100.0% total 69 601 5815

a)

 mean =x̅=Σf*M/Σf=601/69= 8.71

b)

median =middle value =(n+1)/2 th value =(69+1)/2 th value =35 th value =9

c)

 sample Var s2=(ΣfM2-ΣfM2/n)/(n-1)= 8.5324 Std deviation s= √s2 = 2.921

d) first quartile =npth value=69*0.25 th value =17.25th value ~ 18th value =6

e)

third quartile =npth value=69*0.75 th value =51.75th value ~ 52th value =11

f)

percent of the respondents have at least 13 pairs of Shoes =(10/69)*100=14.49 %

g)

18% of all respondents have fewer than how many pairs of Shoes =6

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