Solving Word Problems Involving Chebyshev's Theorem

Updated on March 7, 2018
Source

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.

© 2012 Maria Cristina Aquino Santander

Comments

    0 of 8192 characters used
    Post Comment

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      10 days ago from Manila

      Thanks for appreciating this hub. Good day !

    • profile image

      thanks for appreciating this solution 

      6 weeks ago

      Thanks for appreciating this solution

    • profile image

      seid hansar 

      6 weeks ago

      i like it

    • profile image

      Cristina Santander 

      2 months ago

      Thanks for dropping by. Stay blessed.

    • profile image

      saleem 

      2 months ago

      this is very usefull for me

      thanks author of this site

    • profile image

      Steve Sebastian (KNUST) 

      3 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

    • profile image

      Sijo 

      2 years ago

      Thank you for the questions Ma'am

    • jpcmc profile image

      JP Carlos 

      6 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.

    • cristina327 profile imageAUTHOR

      Maria Cristina Aquino Santander 

      6 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.

    • jpcmc profile image

      JP Carlos 

      6 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

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, owlcation.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://owlcation.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)