TAKE-HOME ASSIGNMENT # 3A
NAME
ANSWER KEY
GRADE
/ 100
1.
Please put your name in the space above.
Do this for every assignment.
2.
Copy your answers directly from your Class Notes to this file, by
PASTING
your respective table
directly
BELOW
each of the reference tables provided here you will save some time.
3.
DO NOT ELIMINATE THE REFERENCE TABLES!
They are your reference points to be sure
you have answered all the questions AND will also be used to show corrections to your answers.
4.
When you save your work, please remember to rename the TH file by adding your last and first
name.
For example
: TH3-JonesP
5.
NOTE TH3 DUE DATE: SUNDAY MIDNIGHT
Feb. 25
3-2-6
Find the mean of 3,24,30,47,43,7,47,13,44,39.
x
x
n
=
∑
Σ
x
=
3+ 24+30+47+43+7+47+13+44+39 = 297 cg
n
=
10 SAMPLES
Σ
x/n
=
(297/10)
x
=
29.7 cg
Is the cereal sugar content MEAN representative of American consumption?
Why?
No.
The mean sugar content would be representative if the sampling size was larger, selected
randomly within each brand of cereal and selected in a manner that was representative of the cereal
actually consumed by the population or by selected portions of the population (children vs adults).
3-2-6
Find the median of 3,24,30,47,43,7,47,13,44,39.
Reorder the data:
3,7, 13, 24 30, 39, 43, 44, 47, 47
Median numbers:
30 + 39
Average of median numbers
: (30+39)/2 = 34.5 cg
Is the cereal sugar content MEDIAN representative of American consumption?
Why?
No. The same reasons as above plus the additional problem of selecting median numbers only to
represent your sample. If the sampling is not a perfect NORMAL bell curve distribution then the
median numbers will be skewed and less representative of the actual consumption.
Median – Mean = 34.5 – 29.7 = 4.8 cg
difference
3-2-6
Find the mode of 3,24,30,47,43,7,47,13,44,39.
M = 47 cg
where 47 cg is the most often repeated number.
Is the cereal sugar content MODE representative of American consumption?
Why?
NO.
Compared to the mean and the median, the mode is even more skewed.
The mean calculation is
still our best estimate given the small sample size.
Mode – Mean = 47-29.7 = 17.3 cg difference.
3-2-6
Find the MIDRANGE of 3,24,30,47,43,7,47,13,44,39.
Lowest number:
3
Highest number:
47
Midrange calculation:
(3 + 47)/2 = 25 cg
Is the sugar content MIDRANGE representative of American consumption?
Why?
No.
Where the median and mode are higher than the average, the midrange value is actually lower than
the average.
By calculating the midrange, mode and median we can show that the mean is definitely
the most “average” value. Relatively speaking, the mean is still the best estimate, despite the small
sample size
Midrange – Mean = 25 – 29.7 =
-4.7 cg difference
1