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Question
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10 . If the number of 9 s in the nth row is for each from 1 to 10 , what is the average (arithmetic mean) of all the numbers in the table?
Answer Choices
- A.9.45
- B.9.50
- C.9.55
- D.9.65
- E.9.70
Steps
| Explanation | Calculations | Help |
|---|---|---|
We first note that each entry is either "9" or "10", and that in the "nth row", the number of "9"s is "n - 1". | ||
We then calculate the sum of the entries in the "nth row". | ||
We observe that the row sums from "n = 1" to "n = 10" form an evenly spaced list, so by Average and Median Property of Evenly Spaced Sets the average of these sums is the mean of the first and last values. | Theory & Tactics Method Card EVEN1-C Click to view full details | |
We then find the overall average by dividing the total sum by the total number of entries. |
Scroll horizontally to view all columns
Final Answer
9.55
Question
In a numerical table with 10 rows and 10 columns, each entry is either a 9 or a 10 . If the number of 9 s in the nth row is for each from 1 to 10 , what is the average (arithmetic mean) of all the numbers in the table?
Answer Choices
- A.9.45
- B.9.50
- C.9.55
- D.9.65
- E.9.70
Steps
| Explanation | Calculations | Help |
|---|---|---|
We first note that each entry is either "9" or "10", and that in the "nth row", the number of "9"s is "n - 1". | ||
We then calculate the sum of the entries in the "nth row". | ||
We observe that the row sums from "n = 1" to "n = 10" form an evenly spaced list, so by Average and Median Property of Evenly Spaced Sets the average of these sums is the mean of the first and last values. | Theory & Tactics Method Card EVEN1-C Click to view full details | |
We then find the overall average by dividing the total sum by the total number of entries. |
Scroll horizontally to view all columns
Final Answer
9.55