Average Mean or Arithmetic Mean

1. (a) Define

A. Mean

B. Median

C. Mode

D. Standard deviation.

(b) Find the mean and mode of the following set of data A. 2, 3, 5, 7, 9, 9, 10, 11, 14, 18

B. 3, 5, 8, 10, 12, 15, 16 . 2, 3, 4, 4, 5, 5,7,7,7,9

A. Mean: The sum of all values in a dataset divided by the number of values. It gives the average value.

B. Median: The middle value in a dataset when it is arranged in order. If there’s an even number of values, it’s the average of the middle two.

C. Mode: The value that appears most frequently in a dataset.

D. Standard deviation: A measure of the amount of variation or dispersion in a set of values. It indicates how spread out the values are from the mean.

(b) For the given sets of data:

A. Mean: (2 + 3 + 5 + 7 + 9 + 9 + 10 + 11 + 14 + 18) / 10 = 8.8
Mode: The mode is 9 since it appears twice, which is more frequent than other values.

B. Mean: (3 + 5 + 8 + 10 + 12 + 15 + 16 + 2 + 3 + 4 + 4 + 5 + 5 + 7 + 7 + 7 + 9) / 17 = 6.06 (approx)
Mode: The mode is 7 since it appears three times, which is more frequent than other values.

1. The arithmetic average is also known as the _______.
   a) Sum
   b) Mean
   c) Median
   d) Range

2. To find the average, you need to _______ all the numbers in the set.
   a) Add
   b) Subtract
   c) Multiply
   d) Divide

3. After adding the numbers, you _______ by the total count to get the average.
   a) Add
   b) Subtract
   c) Multiply
   d) Divide

4. What is the average of 10, 15, and 20?
   a) 10
   b) 15
   c) 18.3
   d) 20

5. If you have five numbers and their sum is 40, the average is _______.
   a) 5
   b) 8
   c) 10
   d) 15

6. The arithmetic average helps find the _______ value in a set of numbers.
   a) Maximum
   b) Minimum
   c) Median
   d) Typical

7. To find the average, you _______ the sum by the total number of values.
   a) Multiply
   b) Subtract
   c) Divide
   d) Add

8. What is the average of 5, 10, 15, and 20?
   a) 10
   b) 12.5
   c) 15
   d) 20

9. The average of identical numbers in a set is always _______.
   a) The smallest number
   b) The largest number
   c) The same as each number
   d) Zero

10. If you add five numbers and get a sum of 75, their average is _______.
    a) 10
    b) 15
    c) 25
    d) 75

11. The arithmetic average is sensitive to extreme values, also known as _______.
    a) Outliers
    b) Inliers
    c) Medians
    d) Averages

12. What is the average of 3, 6, 9, and 12?
    a) 6
    b) 8
    c) 10
    d) 12

13. The sum of deviations from the average is always _______.
    a) Negative
    b) Positive
    c) Zero
    d) Equal to the average

14. If you have three numbers with an average of 20, their total sum is _______.
    a) 40
    b) 50
    c) 60
    d) 70

15. The formula to calculate the average is _______.
    a) Total sum ÷ Number of values
    b) Total sum × Number of values
    c) Total sum + Number of values
    d) Total sum − Number of values