Over a nine-month period, OutdoorGearLab tested hardshell jackets designed for ice climbing, mountaineering, and backpacking. Based on the breathability, durability, ver-satility, features, mobility, and weight of each jacket, an overall rating ranging from 0 (lowest) to 100 (highest) was assigned to each jacket tested. The following data show the results for 20 top-of-the line jackets (OutdoorGearLab website, February 27, 2013). 42 66 67 71 78 62 61 76 71 67
61 64 61 54 83 63 68 69 81 53
a. Compute the mean, median, and mode.
b. Compute the first and third quartiles.
c. Compute and interpret the 90th percentile.

(a) The mean is 65.9, the median is, 66.5 and the mode is. 61.

(b) The first and third quartiles are 61 and 71 respectively.

(c) The value of the 90th percentile is, 78.3.

Step-by-step explanation:

The ratings of 20 top-of-the line jackets, arranged in ascending order are as follows:

S = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66 , 67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}

(a)

Compute the mean as follows:

Compute the median as follows:

For an even number of values the median is the average of the middle two values.

Compute the mode as follows:

The mode of a dataset is the term that occurs most of the time.

Thus, the mean is 65.9, the median is, 66.5 and the mode is. 61.

(b)

The first quartile is the median of the first half of the data set.

S₁ = {42 , 53 , 54 , 61 , 61 , 61 , 62 , 63 , 64 , 66}

The third quartile is the median of the second half of the data set.

S₂ = {67 , 67 , 68 , 69 , 71 , 71 , 76 , 78 , 81 , 83}

Thus, the first and third quartiles are 61 and 71 respectively.

(c)

The pth percentile is a data value such that at least p% of the data set is less-than or equal to this data value and at least (100 - p)% of the data-set are more-than or equal to this data value.

Use the Excel formula "=PERCENTILE.INC(array,0.9)" to compute the 90th percentile.

The value of the 90th percentile is, 78.3.

This value implies that 90% of the ratings are less than 78.3.

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!