Download - Trail Mix Statistics
Trail Mix StatisticsBy Tyler Lipshutz
About Trail MixMade with dried fruits, grains, nuts,
and sometimes chocolateIdeal for long outdoor hikes1968 when first invented in CaliforniaGORP, “Good Old Raisins and Peanuts”PlantersEmeraldArcher FarmsThird Party brands (Wegmans)
My Goal:Is the distribution in serving sizes
equal to the entire bag? Does the bags overall weight distribute equal to the estimated amount of servings?
How I collected my dataTwo different trail mixes
◦Planters & Wegmans◦$1.59/ 6 oz. & $4.69/ 16 oz.
Count the amount in each bagFind the weight of the servingPick one random piece and count
how many were in that serving.Record data into charts
Distribution of Pieces – Planters.Peanuts (53%)Raisins(24%)M&Ms(17%)Almonds(3%)Cashews(3%) Peanuts
53%
M&Ms17%
Cashew s3%
Raisins24%
Almonds3%
Peanuts M&Ms Cashew s Raisins Almonds
Distribution of Pieces – Rainbow DelightPeanuts (59%)Raisins(14%)M&Ms(21%)Almonds(3%)Cashews(3%)
Peanuts M&Ms Cashews Raisins Almonds
Brand vs. WeightShape:
◦ Both are roughly unimodal, P has two peaks around 34 g and 46 g with a gap at 36. RD has peaks at 32 g and 42 g and a gap at 43.
Center: Planters has a center at 34. 9 g. RD has a center at 36.0323 g.
Spread: Planters has a wider spread with a range of 41 and RD has a range of 27.
Rainbow Delight Serving Weight (g)
Weight_g_RD
36.0323213135414831
6.61052S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = countS8 = stdDev
Planters Serving Size Weight (g)
Weight_g_P
34.9122834435330
9.23767S1 = meanS2 = minS3 = Q1S4 = medianS5 = Q3S6 = maxS7 = countS8 = stdDev
Product
0
1
2
3
4
5
6
P
1
2
3
4
5
6
RD
Weight_g0 10 20 30 40 50 60
Trail Mix Histogram
Quantitative Data – Product vs. PeanutsShape: Planters is right
skewed and RD is close to unimodal
Center: Planters mean is 17.2 and RD is 21.1667
Spread: Planters has the greater spread with a range of 17 but Rainbow Delight has a range of 14. Planters has a stdDev of 7.4632 and Rainbow Delight has a stdDev of 5.1929.
PR
DPeanuts
0 5 10 15 20 25 30
Trail Mix Box Plot
Trail Mix
Column Summary
Peanuts
P
RD
Product
517.2
1112132228
621.1667
1516
21.52429
1119.3636
1113212429
S1 = countS2 = meanS3 = minS4 = Q1S5 = medianS6 = Q3S7 = max
Quantitative Data – Product vs. M&MsShape: Both are slightly
unimodalCenter: Planters mean is
4.33 and RD is 7.625Spread: Both have the same
range of 9 so they are equally wide. Planters has a stdDev of 3 and Rainbow Delight has a stdDev of 2.92.
Overall both have an equal spread but Planters has a much lower amount of M&Ms per serving size than Wegman’s Brand
PR
D
MMs0 2 4 6 8 10 12 14
Trail Mix Box Plot
Trail Mix
Column Summary
MMs
P
RD
Product
94.33333
034693
87.625
45.57.5
913
2.92465
175.88235
0468
133.33321
S1 = countS2 = meanS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s
Quantitative Data – Product vs. Cashews Shape: Planters has a right skew
but the shape of RD looks unimodal Center: Planters mean is 1.25 and
RD is 2.714 Spread: Rainbow Delight has a
higher range of 6 which means a wider spread when compared to Planters with has a range of 4. Planters has a stdDev of 1.8929 and Rainbow Delight has a stdDev of 2.058.
Overall, both have little average amounts of cashews in them when compared to other pieces but of these two brands Wegman’s brand has a larger average cashews.
Trail Mix
Column Summary
Cashews
P
RD
Product
41.25
00
0.52.5
41.89297
72.71429
01246
2.05866
112.18182
00246
2.0405S1 = countS2 = meanS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s
PR
DCashews
0 1 2 3 4 5 6 7
Trail Mix Box Plot
Quantitative Data – Product vs. Raisins Shape: Both brands look
unimodal for Raisins Center: Planters mean is 9.333
and RD is 18.5 Spread: Rainbow Delight has a
smaller range of 3 but Planters is much wider with 9. Planters has a stdDev of 3.559 and Rainbow Delight has a stdDev of 1.29.
Overall, Rainbow Delight’s average is higher than Planters per serving but there only 4 samples from Rainbow delight so the data might not be justified.
PR
D
Raisins0 2 4 6 8 10 12 14 16 18 20 22
Trail Mix Box Plot
Trail Mix
Column Summary
Raisins
P
RD
Product
69.33333
56
9.51214
3.55903
418.5
1717.518.519.5
201.29099
101358
131820
5.47723S1 = countS2 = meanS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s
Quantitative Data – Product vs. Almonds Shape: Planters is right
skewed but RD looks unimodal Center: Planters mean is
2.6667 and RD is 4.8333 Spread: Rainbow Delight has
a larger range of 9 but Planters is smaller with 5. Planters has a stdDev of 1.751 and Rainbow Delight has a stdDev of 3.430.
Overall, Rainbow Delight’s average is higher than Planters per serving and RD’s mean matches Planter’s max and the Q1 for both are the same at 2.
PR
D
Almonds0 2 4 6 8 10 12
Trail Mix Box Plot
Trail Mix
Column Summary
Almonds
P
RD
Product
62.66667
02
2.545
1.75119
64.83333
12
4.57
103.43026
123.75
023
5.510
2.83244S1 = countS2 = meanS3 = minS4 = Q1S5 = medianS6 = Q3S7 = maxS8 = s
1 Samp T Interval Conditions: SRSPop>10nNormal Pop
or > 30
Random weighing
There are more than 300 servings of trail mix; there is more than 310 servings of trail mix
30>30; 31>30Conditions Med >> Students’ t-model >> 1 Samp T Interval
1 Sample T Interval: Rainbow Delight weight per serving
N = 31, df = 30Sample mean = 36.032336.0323 + 2.424We are 95% confident that the true
mean of grams per serving of Wegmans Trail Mix from Wegmans is between 33.6075 and 38.457
1 Sample T Interval: Planters Trail Mix weight per serving
N = 30, df = 29Sample mean = 34.934.9 + 3.449We are 95% confident that the true
mean of grams per serving of Planters Trail Mix from Wegmans is between 31.451 and 38.451
Chi-Squared GOF ConditionsCategorical
Data?SRS?All expected cell
counts > 5?
Yes, bothStated, bothYes all expected
for both > 5
(218-76.4)²+(60-76.4)²+…=398.49476.44 76.4 76.4
P( >398.4947|df=4)= 5.88x10-85
Ho: The observed frequency distribution of pieces fits the expected distribution.
We reject the Ho because our p-value is < alpha which is .05. We have sufficient evidence that the observed frequency distribution of pieces does not fit the expected distribution.
Chi-Squared GOF Test - Planters
Ha: The observed frequency distribution of pieces does not fit the expected distribution
Peanuts M&Ms Cashews Raisins AlmondsPieces/Bag 218(76.4) 60(76.4) 6(76.4) 91(76.4) 6(76.4)
(636-217.1)²+(226.5-217.1)²+…=1131.527867 217.1 217.1
P( >1131.527867|df=4)= 0
Ho: The observed frequency distribution of pieces fits the expected distribution.
We reject the Ho because our p-value is < alpha which is .05. We have sufficient evidence that the observed frequency distribution of pieces does not fit the expected distribution.
Chi-Squared GOF Test – Rainbow Delight
Ha: The observed frequency distribution of pieces does not fit the expected distribution
Peanuts M&Ms Cashews Raisins Almonds
Pieces/Bag 636(217.1)226.5(217.
1) 38(217.1)151.5(217.
1)33.5(217.1
)
Bias & ErrorSome peanuts were still together
while others were split in half◦ I counted both as one(1).
Raisins were sometimes conjoined
While counting one would fall on the floor
Human error of counting/Loss of Precision
I got hungry !
Personal Opinions & ConclusionPlanters is tastierMore convenient than a giant tubBased of the GOF tests, neither have
uniformly distributed pieces.The Rainbow Delight has an accurate
serving size based on the confidence interval and the claim on the tub.
The serving size for Planters is higher based on the confidence interval compared to the claim on the bag.