Question

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	Frequency
1	2
2	5
3	6
4	13
5	13
6	1

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. Complete the columns of the chart. (Round your answers to three decimal places.)

X	Frequency	Relative Frequency	Cumulative Relative Frequency
1	2
2	5
3	6
4	13
5	13
6	1

D. Find the first quartile.

E. Find the median.

F. Find the third quartile.

G. Construct a box plot of the data.

H. What percent of the students owned at least five pairs? (Round your answer to one decimal place.)

I. Find the 40^th percentile.

J. Find the 90^th percentile.

Answer 1

solution : Frequency (x,- 71 | (8 - x)?f 8.6029 16.0178 3.3489 16.7445 0.6879 41334 0.0289 0.3757 1.3 689 17.7957 4.7089 4.7089 <fx1=153 ECX-65:f - 59.776 A The Sample mean X = Exe.fr = 153 40 = 3.825 B) the sample. Standard deviation E (x₂-x)"f

S-59.776 40 = 51.4944 c)2224 ~ 1.22 D) The first quartile = ky - 1x40 is 2. .. First quartile ..: Q1=2. median - 5+6 from table Middle valeres i 25.5 F) the third quarhite iD 13 I since 2 5.6 13 1 5.5 median

H) The percent of students owned Five pairs is P(x 750 = P(x=5) + P(x=6) 40 20.35 = 35% 35% of students owned five pairs. h 40th percentile Puo - 40(n+19 100 = 40(40+) 100 - 16.4 th term e This corresponds x=u :Puo = 4) aoth percentile Pora 90(n+1) too = 90090+1) J 100 = 36.9 th ter