Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows:

X Frequency1 32 43 74 125 126 2

a.) Find the sample mean x. (Round your answer to two decimal places.)b.) Find the sample standard deviation, s. (Round your answer to two decimal places.)c.) Find the first quartile. d.) Find the median. e.) find the 3rd quartilef.) What percent of the students owned at least five pairs? (Round your answer to one decimal place.)g.) Find the 40th percentile. h.) find the 90th percentile

a) sample mean = 3.8

b) s = 0.68

c) first quartile = 3

d) median = 4

e) third quartile = 5

f) students owned at least five pairs = 35%

g) The 40th percentile = 4 pairs

h) The 90th percentile = 5 pairs

Given information:

There are total 40 students.

X = the number of pairs of sneakers owned

X Frequency  

1 3  

2 4  

3 7  

4 12  

5 12  

6 2

Step-by-step explanation:

3 students owned 1 pair of sneakers

4 students owned 2 pair of sneakers

and so on....

Therefore, data can also be shown like this

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, | 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6

a) Find the sample mean

sample mean = (1*3+2*4+3*7+4*12+5*12+6*2)/40  

sample mean = 152/40 = 3.8

b) Find the standard deviation

= ∑

where is called variance and is the standard deviation

Putting the values in the above equation yields

s² = 18.04/39 = 0.462

s = = 0.68

c) Find the first quartile

The first quartile is the middle value between starting point and median point.

The median point is 40/2 = 20th value

The first quartile is 20th - 10 = 10th value

1, 1, 1, 2, 2, 2, 2, 3, 3, 3,<= 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6

Hence the first quartile is = 3

d) Find the median

The median is 40/2 = 20th value

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, <= 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6

Hence the median is = 4

e) find the 3rd quartile

The third quartile is the middle value between median point and ending point.

The median point is 40/2 = 20th value

The third quartile is 20th + 10th = 30th value

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5,<= 5, 5, 5, 5, 5, 5, 5, 5, 6, 6

Hence the third quartile is = 5

f) What percent of the students owned at least five pairs?

students owned at least five pairs = students who owned five or more pairs

There are 12 students who owned 5 pairs = 12/40 = 0.30 = 30%

There are 2 students who owned 6 pairs = 2/40 = 0.30 = 0.05 = 5%

students owned at least five pairs = 30% + 5% = 35%

g) Find the 40th percentile

n = (P/100)*n

n = (40/100)*40

n = 16th value

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4,<= 4, 4, 4, 4, | 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6

The 16th value in the data is 4 pairs.

This means that 4 pairs of sneakers is the 20th percentile of the students.

20 percent have 4 pairs of sneakers or lower.

h) find the 90th percentile

n = (P/100)*n

n = (90/100)*40

n = 36th value

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, | 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,<= 5, 5, 6, 6

The 36th value in the data is 5 pairs.

This means that 5 pairs of sneakers is the 90th percentile of the students.

90 percent have 5 pairs of sneakers or lower.

answer: true

step-by-step explanation: