# Solving Word Problems Involving Chebyshev's Theorem

**Solving Word Problems Involving Chebyshev’s Theorem**

**Chebyshev’s Theorem states that the proportion or percentage of any data set that lies within k standard deviation of the mean where k is any positive integer greater than I is at least 1 – 1/k^2.**

**Sample Problem Number One :**

**The mean score of Insurance Commission Licensure Examination is 75 with a standard deviation of 5. What percentage of the data set lies between 50 and 100 ?**

**Solution : First find the value of k**

**Mean – (k) (sd) = lower limit**

**75 – 5K - 50**

**75 – 50 = 5k**

**25 = 5k**

**K = 5**

**To get the percentage use 1 – 1/k^2**

**1 - 1/ 25 = 24/25 = 96%**

**96% of the data set lies between 50 and 100.**

**Sample Problem Number Two :**

**The mean age of flight attendant of PAL is 40 years old with a standard deviation of 8. What percent of the data set lies between 20 and 60 ?**

**Solution : First find the value of k**

**40 – 20 = 8k**

**20 = 8k**

**k = 2.5**

**To find the percentage : 1 – 1/(2.5)^2 = 84 %**

**84% of the data set lies between the ages 20 and 60.**

**Sample Problem Number Three :**

**The mean age of saleslady in ABC Dept Store is 30 with a standard deviation of 6 . Between which two age limit must 75% of the data set lie ?**

**Solution : First find the value of k**

**1 - 1/k^2 = ¾**

**1 - ¾ = 1/k^2**

**¼ = 1/k^2**

**k^2 = 4**

**k = 2**

**Lower age limit :**

**30 - (k ) (sd) = 30 - (6)(2) = 30 -12 = 18**

**Upper age limit :**

**30 + ( k) (sd) = 30 + (6)(2) = 30 + 12 = 42**

**The mean age of 30 with an sd of 6 must lie between 18 and 42 to represent 75% of the data set.**

**Sample Problem Number Four :**

**The mean score in an accounting test is 80 with a standard deviation of 10. Between which two scores must this mean lie to represent 8/9 of data set ?**

**Solution : Find first the value of k**

**1 - 1 /k^2 = 8/9**

**1 - 8/9 = 1/k^2**

**1/9 = 1/k^2**

**k^2 = 9**

**k = 3**

**Lower limit :**

**80 – (10)(3) = 80 – 30 = 50**

**Upper limit :**

**80 + 30 = 110**

**The mean score of 60 with an sd of 10 must lie between 50 and 110 to represent 88.89% of the data set.**

## More by this Author

- 3
Solving Number Problems Involving System of Equations In Two Variables One of the most common applications of equations are number problems. This hub presents five number problems involving system of equations in...

- 21
Solving Problems Involving Angular Velocity Among the challenging problems I encounter in Trigonometry are problems involving angular velocity. In this hub, I presented several problems...

- 108
TOPIC: PROBLEM SOLVING INVOLVING RATIONAL EQUATION FEATURING: WORK PROBLEM MOTION PROBLEM TOPIC OBJECTIVES: At the end of the lesson the students are expected to: 1. Gain skill in solving...

## Comments 4 comments

This brings back painful memories. But it's nice to review numbers once again. I just don't know why I took an extra elective in math class in 3rd year high school. I'm a certified nerd!

But seriously, I use SPSS for any staistical computation I need for work. Of course doing it the old fashioned manual computation is important.

Thanks for the clear discussion. I need to bookmark this hub.

I like math though I'm not good at it. I use stat especially when I do my Training Needs analysis. I need to back up my training proposals with hard facts. Statistics often gets the training approved.

Thank you for the questions Ma'am