Question

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

57 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 4 5 6 7 8 9 10 11
Frequency 7 8 9 9 5 5 6 8

Round all your answers to 4 decimal places where possible.

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 6 pairs of Shoes? %

13% of all respondents have fewer than how many pairs of Shoes?

Homework Answers

Answer #1
x f f*m f*m2 cf
4 7 28 112 7
5 8 40 200 15
6 9 54 324 24
7 9 63 441 33
8 5 40 320 38
9 5 45 405 43
10 6 60 600 44
11 8 88 968 51
total 57 418 3370
mean =x̅=Σf*M/Σf= 7.3333
sample Var s2=(Σfm2-(Σfm2)/n)/(n-1)= 5.4405

the mean is Σxf/Σf =(4*7+5*8+6*9+7*9+8*5+9*5+10*6+11*8)/57 =7.3333

median =middle value =(57+1)/2 th value =29 th value =7

sample standard deviation √5.4405 =2.3325

first quartile =middle value of lower half =(14th +15th value)/2 =5

third quartile is=middle value of upper half =(43th +44th value)/2 =(9+10)/2 =9.5

percent of the respondents have at least 6 pairs of Shoes =(24/57)*100=42.1053%

13% of all respondents have fewer than how many pairs of Shoes =5

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