Can someone help me do this im so cunfeused and dont know how to do it
1. find the mean, varience and standard deviation for the following data set
49,32,35,43,45,40,53,55,42
2.identify the inverse of the following function
h(x)= 1 + 1/2x
1. - for the mean, add them up and then divide by 9
- for the variance: for each number, take the difference between that number and the mean from you first step. Now square that difference, finally add up all those squares and divide that sum of squares by 9.
- for the standard deviation, take the square root of the variance.
Check with your text or your notes or your instructor if you are dividing by 9 or by 8. There are two ways of doing this, check which method you are using.
2. let y = 1 + 1/(2x) <----- I assumed the denominator is 2y, you need those brackets.
step1: interchange the x and y variables.
y = 1 + 1/(2x) -----> x = 1 + 1/(2y)
step2: solve this new equation for y
2xy = 2y + 1
2xy - 2y = 1
y(2x - 2) = 1
y = 1/(2(x-1)) or 1/(2x - 2)
but idk how to actually do it like i get the work but dont really know how to solve it if that makes sense?
No, it does not make sense to me that somebody taking this kind of
math cannot add 9 simple number, and then divide that by 9
It does not make sense to me that somebody taking this kind of
math cannot subtract one number from another, then square it .....
Now for the sum of the squares:
(assume your mean to the first part was 45, IT IS NOT)
49-45 = 4 , square that: (4)^2 = 16
32-45 = -13, square that: (-13)^2 = 169
35-45 = -10, square that: (-10)^2 = 100
.....
now add up 16 + 169 + 100 + ..... = .......
Divide that sum by 9
and you got your variance! (read my final part above about ÷ 9 or ÷ 8)
It does but ok
1. To find the mean, variance, and standard deviation for a given data set, you'll need to follow these steps:
a. Find the mean (average) by adding up all the values in the data set and dividing by the number of values.
b. Subtract the mean from each individual value in the data set, square the result, and sum up all the squared differences.
c. Divide the sum of squared differences by the total number of values in the data set to find the variance.
d. Take the square root of the variance to find the standard deviation.
Let's apply these steps to the given data set:
a. Mean: add up all the values and divide by the total number of values:
(49 + 32 + 35 + 43 + 45 + 40 + 53 + 55 + 42) / 9 = 394 / 9 ≈ 43.7778 (rounded to four decimal places)
b. Calculate the squared difference from the mean for each value:
(49 - 43.7778)^2 + (32 - 43.7778)^2 + (35 - 43.7778)^2 + (43 - 43.7778)^2 + (45 - 43.7778)^2 + (40 - 43.7778)^2 + (53 - 43.7778)^2 + (55 - 43.7778)^2 + (42 - 43.7778)^2 = ...
[you can calculate this result]
c. Divide the sum of squared differences by the total number of values to find the variance:
variance = [result from previous step] / 9 = ...
d. Take the square root of the variance to find the standard deviation:
standard deviation = sqrt(variance) = sqrt([variance value]) = ...
2. To find the inverse of a function, you need to swap the roles of the dependent and independent variables and solve for the original independent variable.
Let's find the inverse of the given function, h(x) = 1 + 1/2x:
a. Replace h(x) with y: y = 1 + 1/2x.
b. Swap the roles of x and y: x = 1 + 1/2y.
c. Solve the equation for y: Subtract 1 from both sides to isolate 1/2y, then multiply both sides by 2 to solve for y.
2x - 2 = 1/2y
y = 2(2x - 2) = ...
The inverse of the function h(x) = 1 + 1/2x is given by y = 2(2x - 2).