Math Problem Statement

Find the average of the following number sequence: 203, -8, 205, 227, 16, 229, 251, 40, 253, ..., 995, 784, 997.

Solution

To find the average of the given number sequence, we need to follow these steps:

Steps:

  1. Add up all the numbers in the sequence to get the total sum.
  2. Count how many numbers are in the sequence.
  3. Divide the total sum by the number of elements to get the average.

The sequence given is:

203,8,205,227,16,229,251,40,253,,995,784,997203, -8, 205, 227, 16, 229, 251, 40, 253, \dots , 995, 784, 997

Let's calculate the average. I'll extract the numbers and calculate the sum and average.

I'll now proceed to calculate this for you.The total sum of the numbers in the sequence is 4,192, and there are 12 numbers in total.

Thus, the average of the sequence is:

419212349.33\frac{4192}{12} \approx 349.33

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:

  1. How do you calculate the average if a sequence contains negative numbers?
  2. Can the average of a sequence be lower than all the numbers in it?
  3. How would you find the median of this sequence?
  4. What happens to the average if you add more numbers to this sequence?
  5. How does the range (difference between the largest and smallest number) relate to the average?

Tip: The average is a useful measure, but it can be skewed by outliers, especially when some numbers are much larger or smaller than the others!

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Math Problem Analysis

Mathematical Concepts

Averages
Arithmetic Mean
Number Sequences

Formulas

Arithmetic Mean = (Sum of terms) / (Number of terms)

Theorems

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Suitable Grade Level

Grades 6-8