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Chapter 4: Problem 31

$$ 650, a, 1550,1750,2300,2650 $$ If the mean of the list above is 1650 , what is the value of \(a\) ?

Short Answer

Expert verified
The value of 'a' is \(900\).

Step by step solution

01

Calculate the sum of given numbers

The list of given numbers without 'a' is: 650, 1550, 1750, 2300, 2650. Let's add these numbers: Sum = 650 + 1550 + 1750 + 2300 + 2650 = \(9000\)
02

Calculate the total sum of the list using the given mean

We are given that the mean of the list is 1650. To find the total sum, we will multiply the mean by the number of items in the list, which is 6 in this case (including 'a'): Total sum = Mean × Number of items = \(1650 × 6 = 9900\)
03

Find the value of 'a'

Now that we have the sum of the given numbers and the total sum of the list, we can find the value of 'a' by subtracting the sum of given numbers from the total sum: Value of 'a' = Total sum - Sum = \(9900 - 9000 = 900\) So, the value of 'a' is \(900\).

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