How do I calculate the value of K using Tchebycheff's theorem for this data?

[masterchiefo]

Homework Statement

Hello all,

I have a one number stat:

Xi
2
4
5
6
6
8
10

Tchebycheff :
It ask me to find the value of K.

Interval of confidence: 89%

I know 1-1/k²
I have no idea how to calculate the value of K.
Do I have to somehow use the interval of confidence?

I checked my book and notes and there is nothing stating how to calculate K.
I just need to know the formula. Thanks.

 

[Ray Vickson]

Homework Statement

Hello all,

I have a one number stat:

Xi
2
4
5
6
6
8
10

Tchebycheff :
It ask me to find the value of K.

Interval of confidence: 89%

I know 1-1/k²
I have no idea how to calculate the value of K.
Do I have to somehow use the interval of confidence?

I checked my book and notes and there is nothing stating how to calculate K.
I just need to know the formula. Thanks.

(1) Your question makes no sense. 89% confidence interval for what? What do you mean by K?
(2) You are required to show your work before getting any help.

 

[masterchiefo]

(1) Your question makes no sense. 89% confidence interval for what? What do you mean by K?
(2) You are required to show your work before getting any help.

This is all I have, no other info from teacher.
trust me I would love to show any work...but...I have no idea what is K. or what is the relation with 89% confidence interval. it probably have no relation and its just there to mess with my head.

All I have is this on my paper:
Fill the blank:

Xi
2
4
5
6
6
8
10

Tchebycheff :
Interval of confidence: 89%
K=

 

[HallsofIvy]

You titled this "Tychebycheff". Are you saying you do not know what Tchebycheff's theorem is? If so did you try looking it up?

Tchebycheff's theorem says that if X is a random variable with mean $\mu$ and standard deviation $\sigma$ then the probability that $|x- \mu|\ge k\sigma$ is less than or equal to $1/k^2$. What are the mean and standard deviation for this data? What are the upper and lower numbers such that 89% of the data is closer to the mean than those?