The jeans project Matt Fuhrman – 9A GAT

The task Travel to 3 stores and measure a minimum of 30 pairs of jeans. Using the data collected from the stores, find out which store has jeans that are truest to their size. All jeans measured were size 32 with a relaxed fit, the reason behind the sizes and fit of the jeans is that there was an abundance of this size and style at the various stores.

The stores Data was collected from three stores, Meijer, K-Mart and Target. Meijer had the least expensive jeans at $14.98 a pair. K-Mart had the middle price of jeans at $19.99 a pair, followed by the jeans at Target that cost $24.99 a pair of jeans, the most expensive. The reason behind the choosing of these stores is that they were close to my house.

The hypothesis It was hypothesized that the jeans measured at Target would be truest to their size. This was hypothesized as the jeans at Target are the most expensive. I believe that since the jeans were the most expensive, more care and precision would be executed in the manufacturing of the jeans. $ $ $ $ $

The Procedures Jeans were measured to the nearest 16th of an inch. First, a collection 12 size-32 relaxed-fit jeans was selected. Then a pair of jeans was held at each side, pulling the waist of the jeans tight. Next, wrap a tape measure around the waist of the pants and made that the tape measure was pulled tight, leaving no space around the jeans and the tape. The tape measure was then wrapped around and the measurement was recorded. This process was done for all 12 pairs at each of the three stores.

THE DATA Data collected from the three stores is expressed in tables on the next three slides. Each table includes the store’s name, manufacturer name, size, measurement, price, and fit. The average measurement for each data set is also included.

THE DATA – 12 jeans were measured at Meijer. Store Manufacturer Size Measurement (inches) Price (dollars) Fit Meijer Falls Creek 32 35 1/4 14.98 Relaxed 36 35 1/8 34 7/8 35 3/4 35 1/2 34 1/8 35 3/8 35   Avg. 35.22 12 jeans were measured at Meijer. Jeans measured at this store ranged from 34 7/8 inches to 35 ¾ inches. Data in this set ranged 1 7/8 inches. The range of data in this set was the greatest out of all of the data sets. The mean of the measurements is 35.22 inches, the highest out of all of the data. Jeans at this store cost $14.98 a pair.

THE DATA – K-MART Store Manufactor Size Measurement (inches) Manufacturer Size Measurement (inches) Price (dollars) Fit K-Mart Wrangler 32 34 3/4 19.99 Relaxed 35 1/2 35 5/8 35 1/8 35 1/4 34 1/8 36 1/4 35 3/4 34 1/2 34 7/8   Avg. 35.18 Store Manufactor Size Measurement (inches) Price (dollars) Fit Meijer Falls Creek 32 35 1/4 14.98 Relaxed 36 35 1/8 34 7/8 35 3/4 35 1/2 34 1/8 35 3/8 35   Avg. 35.22 12 jeans were measured at K-Mart. Jeans measured at this store ranged from 34 1/8 inches to 36 1/4 inches. Data in this set ranged of 1 5/8 inches. The mean of the measurements is 35.18 inches. Jeans at this store cost $19.99 a pair.

THE DATA – Target Store Manufactor Size Measurement (inches) Price (dollars) Fit K-Mart Wrangler 32 34 3/4 19.99 Relaxed 35 1/2 35 5/8 35 1/8 35 1/4 34 1/8 36 1/4 35 3/4 34 1/2 34 7/8   Avg. 35.18 Store Manufactor Size Measurement (inches) Price (dollars) Fit Meijer Falls Creek 32 35 1/4 14.98 Relaxed 36 35 1/8 34 7/8 35 3/4 35 1/2 34 1/8 35 3/8 35   Avg. 35.22 Store Manufacturer Size Measurement (inches) Price (dollars) Fit Target Denizen from Levis 32 34 1/4 24.99 Relaxed 34 3/8 34 1/2 34 3/4 34 7/8 35 35 1/8 35 3/8 35 1/2 35 3/4 35 7/8   Avg. 35.02 12 jeans were measured at Target. Jeans measured at this store ranged from 34 1/4 inches to 35 7/8 inches. Data in this set ranged 1 5/8 inches. The mean of the measurements is 35.02 inches, the lowest of all the data sets. Jeans at this store cost $24.99 a pair.

THE DATA Jeans collected from Meijer had the highest mean. The range of measurements collected from Target was the highest. Measurements at Target had a range of 1 5/8 inches in comparison to K-Mart’s range of 1 5/8 inches and Meijer’s range of 1 7/8.

The box plots "Minimum" 34.13 "Q₁" 34.815 "Median" 35.19 "Q₃" 35.375 "Maximum" 35.75 "Minimum" 34.13 "Q₁“ 35.065 "Median“ 35.25 "Q₃" 35.44 "Maximum" 36 "Minimum" 34.25 "Q₁“ 34.625 "Median“ 34.94 "Q₃“ 35.44 "Maximum" 35.88

The box plots Box plot for Meijer is the only one to contain an outlier. This outlier is on the low end of the figure. Box plot for Meijer also possesses the smallest box, this is due to its smaller deviation in comparison to the other data sets. K-Mart’s median is roughly in the middle of its data. The box plots show that K-Mart’s waist size measurements have a greater range in comparison to the others.

Standard deviation - Standard Deviation = S = √∑(x-x̄)²/n-1 Meijer Data (x) Deviation from mean (x-x̄) Deviation squared (x-x̄)² 1 34.125 34.125 - 35.219 = -1.094 (-1.094)² = 1.196836 2 34.875 34.875 - 35.219 = -0.344 (-0.344)² = 0.118336 3 35.000 35 - 35.219 = -0.219 (-0.219)² = 0.047961 4 35.125 35.125 - 35.219 = -0.094 (-0.094)² = 0.008836 5 6 35.250 35.25 - 35.219 = 0.031 (-0.031)² = 0.000961 7 8 (-0.031)² =0.000961 9 35.375 35.375 - 35.219 = 0.156 (0.156)² = 0.024336 10 35.500 35.5 - 35.219 = 0.281 (0.281)² = 0.078961 11 35.750 35.75 - 35.219 = 0.531 (0.531)² = 0.281961 12 36.000 36 - 35.219 = 0.781 (0.781)² = 0.609961 Total 35.219   ∑(x-x̄)² = 2.32211 Standard Deviation = S = √∑(x-x̄)²/n-1 S = √2.32211/12-1 S = √2.32211/11 S ≈ 0.13853155501 Variance = S² V ≈ 0.13853155501² V ≈ 0.01919099173

Dot PLOT –

Standard deviation - Standard Deviation = S = √∑(x-x)²/n-1 K-Mart Data (x) Deviation from mean (x-x̄) Deviation squared (x-x̄)² 1 34.125 34.125 - 35.177 = -1.052 (-1.052)² = 1.106704 2 34.500 34.500 - 35.177 = -0.677 (-0.677)² = 0.444889 3 34.750 34.750 - 35.177 = -0.427 (-0.427)² = 0.182329 4 34.875 34.875 - 35.177 = -0.302 (-0.302)² = 0.091204 5 35.125 35.125 - 35.177 = -0.052 (-0.052)² = 0.002704 6 7 35.250 32.250 - 35.177 = -2.927 (-2.927)² = 8.567329 8 9 35.500 35.500 - 35.177 = 0.323 (0.323)² = 0.104329 10 35.625 35.625 - 35.177 = 0.448 (0.448)² = 0.200704 11 35.750 35.750 - 35.177 = 0.573 (0.573)² = 0.328329 12 36.250 36.250 - 35.177 = 1.073 (1.073)² = 1.151329 Total 35.177   ∑(x-x)² = 20.749883 Target Data (x) Deviation from mean (x-x̄) Deviation squared (x-x̄)² 1 34.25 34.250 - 34.904 = -0.654 (-0.654)² = 0.427716 2 34.38 34.375 - 34.904 = -0.529 (-0.529)² = 0.279841 3 34.50 34.500 - 34.904 = -0.404 (-0.404)² = 0.163216 4 34.75 34.750 - 34.904 = -0.154 (-0.154)² = 0.023716 5 34.88 34.875 - 34.904 = -0.029 (-0.029)² = 0.000841 6 7 35.00 35.000 - 34.904 = 0.096 (0.096)² = 0.009216 8 35.13 35.125 - 34.904 = 0.221 (0.221)² = 0.048841 9 35.38 35.375 - 34.904 = 0.471 (0.471)² = 0.221841 10 35.50 35.500 - 34.904 = 0.596 (0.596)² = 0.355216 11 35.75 35.750 - 34.904 = 0.846 (0.846)² = 0.715716 12 35.88 35.875 - 34.904 = 0.971 (0.971)² = 0.942841 Total 35.021   ∑(x-x)² = 3.189842 Standard Deviation = S = √∑(x-x)²/n-1 S = √3.189842/12-1 S = √3.189842/11 S ≈ 0.16236480708 Variance = S² V ≈ 0.16236480708² V ≈ 0.02636233057

Dot PLOT –

Standard deviation - Standard Deviation = S = √∑(x-x)²/n-1 K-Mart Data (x) Deviation from mean (x-x̄) Deviation squared (x-x̄)² 1 34.125 34.125 - 35.177 = -1.052 (-1.052)² = 1.106704 2 34.500 34.500 - 35.177 = -0.677 (-0.677)² = 0.444889 3 34.750 34.750 - 35.177 = -0.427 (-0.427)² = 0.182329 4 34.875 34.875 - 35.177 = -0.302 (-0.302)² = 0.091204 5 35.125 35.125 - 35.177 = -0.052 (-0.052)² = 0.002704 6 7 35.250 32.250 - 35.177 = -2.927 (-2.927)² = 8.567329 8 9 35.500 35.500 - 35.177 = 0.323 (0.323)² = 0.104329 10 35.625 35.625 - 35.177 = 0.448 (0.448)² = 0.200704 11 35.750 35.750 - 35.177 = 0.573 (0.573)² = 0.328329 12 36.250 36.250 - 35.177 = 1.073 (1.073)² = 1.151329 Total 35.177   ∑(x-x)² = 20.749883 Standard Deviation = S = √∑(x-x)²/n-1 S = √20.749883/12-1 S = √20.749883/11 S ≈ 0.41410944974 Variance = S² V ≈ 0.41410944974² V ≈ 0.17148663636

Dot PLOT –

The Deviation Of the three sets of data, jeans measured at Meijer had the lowest standard deviation. This means that the jeans at Meijer are closest to their mean of 35.22. The data set with the highest standard deviation was the jeans at K-Mart. The deviation of this set was more than twice as much as the other two sets. The data collected at K-Mart had the highest variance due to having the highest deviation as well. This means that there was a greater distance in between each measurement than the other sets.

The truest to size Target’s jeans had the lowest mean, yet K-Mart’s jeans’ box was smaller than the rest. In K-Mart’s data, the Q1 and Q3 numbers created a box that had more lower numbers compared to the rest. These data points were closer to the size 32. None of the data sets were really close to the size of 32 but were very similar to each other. Jeans measured at Meijer had the lowest standard deviation and variance. This means that there was not much difference in the sizes of the jeans, but these data points were not the closest to size 32.

The Conclusion There were not any problems in regards to the measuring of the pants. All of the jeans measured larger than the size of 32. The hypothesis was that Target’s jeans would be truest to size. The hypothesis was incorrect because jeans measured at K-Mart were the truest to size.

advice for consumers Originally it was hypothesized that the more expensive of the jeans would be truest to size but the data collected does not prove this. From the data collected, jeans from Target were the truest to their size, not by much, but were. In this case, paying more money does not get you a better product. For the jeans closest to their size out of the ones chosen, Denizen from Levi’s purchased at Target is your best bet.

advice for manufacturers From looking at the data collected it can easily be determined that both the size of the pants is not equal to the measurement of the pants, and the measurements of the pants are not consistent whatsoever. When jeans are sewn and pressed, the jeans are not being sewn and pressed consistently the same way. This process is done quickly to mass-produce many jeans. As shown by the data, the jean’s waist is not even when it is folded to be sewn, and not all of the jeans end up having the same measurement. While mass-producing many jeans and working on many jeans at a time may be a good idea for selling many goods, it’s not a good idea for making each product the same and having the size be accurate. Advice that can be given so that a better, more accurate product to be sold is to slow down and create jeans with more precision. Currently, a worker just folds fabric in half and sews it together. If this job is done with more precision and care, jeans could be created more accurately and be true to their size.

Works CITED Jeans. Image. Closet Couture. Web. <http://www.closetcouture.com/uploads/1223997626/med_gallery_456__13753.png> Mar. 2013. Meijer logo. Image. Michican Baby Walks. Web. <http://www.mibabywalks.org/MeijerLogo.jpg>26 Mar. 2013. Kmart logo. Image. BatteryTender. Web. <http://batterytender.com/images/kmart- logo-317x336.jpg> 26 Mar. 2013. Target logo. Image. Take5ADay. Web. <http://www.mibabywalks.org/MeijerLogo.jpg>26 Mar. 2013. EVAN199. "How it's made: Jeans" Online video clip. YouTube. YouTube, 17 Jun. 2007. Web. <http://youtu.be/5DzEpOp2Jy8> 26. Mar. 2013.