Question

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	4	5	6	7	8	9	10	11	12	13
Frequency	6	6	6	10	5	6	8	7	5	10

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 13 pairs of Shoes? % :

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

Answer 1

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 =	2.9210

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