unit 2 special centers; trimmed & weighted mean. let’s look at some data how fast food compare...
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Unit 2Unit 2
Special centers;Special centers;Trimmed & Weighted MeanTrimmed & Weighted Mean
Let’s look at some data How Fast Food CompareCompany Fast Food Total Fat Cholesterol Sodium
Calories (g) (mg) (mg)
Kentucky Fried Chicken Lite 'n Crispy (4 pieces) 198 12 39 354
Burger King Hamburger Deluxe 344 19 55 496
Wendy's Single (plain) 340 15 50 500
Kentucky Fried Chicken Original Recipe (4pieces) 248 15 39 575
McDonald's Chicken McNuggets (6) 270 15 42 580
Arby's Regular Roast Beef 353 15 56 588
Kentucky Fried Chicken Extra Crispy (4 pieces) 324 21 47 638
McDonald's Quarter Pounder 410 20 60 650
McDonald's McLean Deluxe 320 10 47 670
Arby's French Dip 345 12 55 678
Wendy's Chicken (regular) 430 19 70 725
Hardee's Big Deluxe Burger 500 30 79 760
Burger King BK Broiler Chicken 379 18 60 764
McDonald's McChicken 415 20 65 770
Comparing various fast food components of nutrition.
• Calories• Fat• Cholesterol• Sodium
The Mean grams of Fat in the fast foods
Fat(g)
9 15 15 19 24 2910 15 15 19 25 3012 15 15 20 25 3312 15 16 20 26 3613 16 18 20 28 4013 18 18 21 29 61
3.2136
76536
61...12109
n
xx
The Trimmed Mean
Fat(g)
9 15 15 19 24 2910 15 15 19 25 3012 15 15 20 25 3312 15 16 20 26 3613 16 18 20 28 4013 18 18 21 29 61
Do you notice that one particular value is possibly an outlier. In order to better compute a “truer” average we will use a “Trimmed” mean.
The Trimmed Mean
The trimmed mean has the advantage of being relatively resistant to outliers. The trimmed mean is computed just as an ordinary mean . . .except.
a pre-specified percentage of the extremes is omitted.
Consider the 5% trimmed mean. The left-most (lowest) 5% and right-most (highest) 5% of the data are excluded; from the remaining observations the mean is found. So, the 10% most "extreme" data (5% on either side) is omitted before computing the mean.
Trimmed Mean
Fat(g)
9 15 15 19 24 2910 15 15 19 25 3012 15 15 20 25 3312 15 16 20 26 3613 16 18 20 28 4013 18 18 21 29 61
2
8.1
)36)(05(.
36%5
use
oftrim
5% Trim
Drop the 2 smallest & 2 largest values
The Trimmed Mean
Fat(g)
9 15 15 19 24 2910 15 15 19 25 3012 15 15 20 25 3312 15 16 20 26 3613 16 18 20 28 4013 18 18 21 29 61
2.2032
645430
36...1212
n
xx
The Trimmed Mean – you try it
Fat(g)
39 50 60 70 9039 53 60 70 9042 55 60 70 9043 55 60 79 9947 56 60 82 10047 57 65 85 194
n
xx
The Weighted MeanThe Weighted Mean
The weighted meanweighted mean is used when the values in a data set are not all equally represented.
The weighted meanweighted mean of a variable of a variable XX is found by multiplying each value by its corresponding weight and dividing the sum of the products by the sum of the weights.
The Weighted MeanThe Weighted Mean
=
The weighted mean
Xw X w X w X
w w w
wX
w
where w w w are the weights
for the values X X X
n n
n
n
n
1 1 2 2
1 2
1 2
1 2
...
...
, , ...,
, , ..., .
The Weighted Mean
Cost of Shoes($)
Shoe CostNo. Sold
Air Jordan $140 3KD $135 4Kobe $200 1Air Force $85 5Converse $45 9
45.90$22
1990$22
)945...()4135()3140(
w
xwx
The Weighted Mean- using the table
Cost of Shoes($)
ShoeCost(x)
No. Sold(w) wx
Air Jordan $140 3 $420KD $135 4 $540Kobe $200 1 $200Air Force $85 5 $425Converse $45 9 $405
totals 22 $ 1990
45.90$22
1990$
w
xwx