Find the upper quartile, lower quartile, interquartile range, and any outliers for each set of data. 11.3, 28.8, 7.1, 12.7, 19, 16.7, 25.6, 7.1, 17.7, 17.5, 11.3, 2.7, 15.3, 20.8, 15.8

a 17, 11.3, 7.7, no outliers

b.. 19, 11.3, 7.7, no outliers

c. 19, 11.3, 6.7, no outliers

d. 19, 11.3, 7.7, 2.7

b.. 19, 11.3, 7.7, no outliers

Step-by-step explanation:

Our set of data is = {11.3, 28.8, 7.1, 12.7, 19, 16.7, 25.6, 7.1, 17.7, 17.5, 11.3, 2.7, 15.3, 20.8, 15.8) when we sort the set from smallest to the biggest then

{2.7, 7.1, 7.1, 11.3, 11.3, 12.7, 15.3, 15.8, 16.7, 17.5, 17.7, 19, 20.8, 25.6, 28.8]

Median of the set is the middle value in the sorted set, which is 15.8

Upper quartile is the middle value between the median and the highest number of the set, which is 19

Lower quartile is the middle value between the median and the highest number of the set, which is 11.3

Interquartile Range is the distance between Upper quartile and Lower quartile, which is 7.7

Outliers are any number in the set which is smaller then  Lower Quartile - (1.5×Interquartile Range)  and higher than Upper Quartile+(1.5×Interquartile Range)

Lower Quartile - (1.5×Interquartile Range) = 11.3-(1.5×7.7) = -0.25

Upper Quartile+(1.5×Interquartile Range)  = 19+(1.5×7.7) = 30.55.

There is no such number in the set, therefore no outliers in the set

step-by-step explanation:

goog be able to you with that maybe

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

=====================================

part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

=====================================

part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).