The document discusses methods for finding unknown values in data sets to achieve a predetermined measure of central tendency such as average, median, or mode. It explains the substitution and cover-up methods for determining a missing number needed to obtain a specific average. Examples walk through setting up and solving problems to find missing values using these methods.

1. Finding a Unknown Value in
Measures of Central Tendency
•How to find the missing number in a
series of numbers to get a
predetermined average.
•How to find the missing number to
get a specific median and mode

2. Substitution Method
Example:
• If you have 6 + 7 + ? = an average of 7,
what is the missing number?
A. 2 B. 5 C. 8 D. 14
If you have multiple choice answers, you can
substitute in numbers until you find the one
that works.

3. Substitution Method
Example:
• If you have 6 + 7 + ____ = an average of 7, what is the
missing number?
A. 2 B. 5 C. 8 D. 14
(6 + 7 + 2) 3 = 5
(6 + 7 + 5) 3 = 6
(6 + 7 + 8) 3 = 7
(6 + 7 + 14) 3 = 9

4. Cover up Method
Example
(6 + 7 + n) 3 = An average of 7

5. Cover up Method
Example
(6 + 7 + n) 3 = An average of 7
Cover up what is in parenthesis
and ask yourself what number
divided by 3 = 7?
(3 x 7 = 21)

6. Cover up Method
Example: Now we know that…
(6 + 7 + n) 3 = 21
Now simplify what you can.
6+7

7. Cover up Method
Example: Now we know that…
(13 + n) 3 = 21
Now cover up the n and ask
yourself what number plus 13
equals 21? (21 -13)

8. Cover up Method
Since 13 + 8 = 21, then
(6 + 7 + 8) 3 = An average of 7

9. You try it!
• Find the missing number using the substitution
method.
• (4 + 7 + 2 + __ ) 4 = An average of 5
A. 3 B. 7 C. 11 D. 20

10. You try it! ANSWER
• Find the missing number using the substitution
method.
• (4 + 7 + 2 + __ ) 4 = An average of 5
A. 3 B. 7 C. 11 D. 20

11. You try it!
• Find the missing number by using the cover
up method.
• (6 + 3 + 1 + 5 + ____) 5= 6

12. You try it! ANSWER
• Find the missing number by using the cover
up method.
• (6 + 3 + 1 + 5 + 15) 5= 6

13. A little bit more challenging…
• If Lauren made test grades of 84, 96, and
92, what would she have to make on her 4th
test to make sure that she would have an
overall average of 90?

14. A little bit more challenging…
• If Lauren made test grades of 84, 96, and
92, what would she have to make on her 4th
test to make sure that she would have an
overall average of 90.
How would you set up this problem?

15. A little bit more challenging…
• If Lauren made test grades of 84, 96, and 92,
what would she have to make on her 4th test to
make sure that she would have an overall
average of 90.
How would you set up this
problem?
(84 + 96 + 92 + ____ ) 4 = 90

16. Use the cover-up method
• (84 + 96 + 92 + ____ ) 4 = 90
• (84 + 96 + 92 + ____ ) 4 = 90
• (84 + 96 + 92 + ____ ) = 360
• (272 + ____ ) = 360
• The answer is 88

17. Median
• If the Median is 5, then what number is
missing in this set of data?
4, ____, 6
• If the Median is 10, then what number is
missing in this set of data?
• 5, 8, ____, 15

18. Mode
• If the Mode is 4, then what number is
missing in this set of data?
3, 4, 4, 5, 5, 6, 8

19. Range
• If the range is 18, then what number is
missing from this set of data?
3, 7, 12, 18, ____