Question

If the average of 800 numbers is 25 and including 67 new numbers, the average raises to 52, then the approximate average of the new numbers

Answer 1

Answer:

374.39

Explanation:

average of 800 numbers=25

800X25=20,000

including 67 average becomes 52

let average of 67 be x                          

( includes 67 numbers so 800+67=867)

then (20,000+67x) / 867 = 52

then x=374.39

Answer 2

Given,

The average of 800 numbers is 25.

Including 67 new numbers, the average becomes = 52

To find,

The approximate average of the new numbers.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

The average of a set of given data can be calculated as follows;

= (sum of all the observations)/(total number of observations)

Now, according to the question;

The average of 800 numbers is 25

=> (sum of all 800 numbers)/(800 observations) = 25

=> (sum of all 800 observations) = 800×25 = 20,000

=> sum of all 800 observations = 20,000

Now, according to the question, when 67 new numbers are added,

The new average = 52

=> (sum of all 800 numbers + newly added 67 numbers)/(800+67 observations) = 52

=> (sum of all 867 numbers) = 52 × 867 = 45,084

=> (sum of all 867 numbers) = 45,084

Now, the sum of the newly added 67 numbers

= (sum of all 867 numbers) - (sum of all initial 800 numbers)

= 45,084 - 20,000

= 25,084

Now, the average of the newly added 67 numbers

= (sum of the newly added 67 numbers)/(67 observations)

= (25,084)/(67)

= 374.39

Hence, the average of the newly added 67 numbers is equal to 374.39.