# Solving Word Problems Involving Chebyshev's Theorem

Updated on March 7, 2018 A graduate of Master in Education with Mathematics as major from the De La Salle University- Manila, Philippines. A PRC licensed teacher.

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 1 is at least 1 – 1/k^2.

Below are four sample problems showing how to use Chebyshev's theorem to solve word problems.

## Sample Problem One

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

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%

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

## Sample Problem Two

The mean age of a 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?

First find the value of k.

40 – 20 = 8k

20 = 8k

k = 2.5

Find the percentage.

1 – 1/(2.5)^2 = 84%

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

## Sample Problem Three

The mean age of salesladies in an ABC department store is 30, with a standard deviation of 6 . Between which two age limits must 75% of the data set lie?

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

Solution: The mean age of 30 with an standard deviation of 6 must lie between 18 and 42 to represent 75% of the data set.

## Sample Problem Four

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

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

Solution: The mean score of 60 with a standard deviation of 10 must lie between 50 and 110 to represent 88.89% of the data set.

0 of 8192 characters used
• AUTHOR

Cristine Santander

6 months ago from Manila

Thanks to all those who appreciated this hub. Stay blessed.

• Marie

6 months ago

Thank you

• AUTHOR

Cristine Santander

9 months ago from Manila

thanks.

• Shameem Tahseen

9 months ago

Nice and simple examples

• AUTHOR

Cristine Santander

9 months ago from Manila

Thanks for appreciating this hub.

• DAVID KASIRYE-MSc. Development Economics, UGANDA MARTYRS UNIVERSITY

9 months ago

Fantastic lesson

• AUTHOR

Cristine Santander

10 months ago from Manila

Thanks for appreciating this hub.

• SHIVANI TIWARI

10 months ago

Thankyou for uploading it. Very useful and clear all my doubts regarding this theorem

• AUTHOR

Cristine Santander

17 months ago from Manila

Thanks for appreciating this hub. Good day !

• thanks for appreciating this solution

18 months ago

Thanks for appreciating this solution

• seid hansar

18 months ago

i like it

• Cristina Santander

19 months ago

Thanks for dropping by. Stay blessed.

• saleem

19 months ago

this is very usefull for me

thanks author of this site

• Steve Sebastian (KNUST)

20 months ago

Wow, to be frank this by far the best site for chebyshev's theory explanation. Examples are on point and clear. I really love this site

• Sijo

3 years ago

Thank you for the questions Ma'am

• JP Carlos

7 years ago from Quezon CIty, Phlippines

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.

• AUTHOR

Cristine Santander

7 years ago from Manila

Hi jpcmc I am glad to hear from you again. Great to see you on this hub. Thank you for dropping by and appreciating this hub. Your visit and comments are much appreciated. Sometimes we have to do the old fashioned manual computation to appreciate Statistics better. I find Statistics a very practical Mathematics. Statistics has sought wide range of applications in business and even in our day to day activities. Blessings to you always and to your family. Best regards.

• JP Carlos

7 years ago from Quezon CIty, Phlippines

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.

working