Question

What's the temperature? The temperature in a certain location was recorded each day for two months. The mean temperature was

52.1°

F with a standard deviation

2.5°

F. What can you determine about these data by using Chebyshev's Inequality with

=K2

?

At least % of the days had temperatures between °F and °F

Answer 1

The temperature in a certain location was recorded each day for two months. The mean temperature was 52.1°F with a standard deviation = 2.5° F.

Now according to Chebyshev's Inequality the proportion of data that lie between K standard deviation is calculated as:

=> 1- 1/K²

Now if K = 2 the the percentage is calculated as:

=> (1- 1/2² )* 100 = 75%

and the values within which the 75% of value lies is calculated by K formula as:

and

Thus At least 75% of the days had temperatures between 47.1 °F and 57.1 °F.

Note: Feel free to ask if any query remains