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Analysis of Recipe Activation Times: Means, Standard Deviations, and IQR, Assignments of Statistics

University of Washington (UW) - BothellStatistics

An analysis of the activation times for different recipe types (a, b, c, and d). It includes the means, standard deviations, and interquartile ranges (iqr) for each recipe type. The document also compares and contrasts the activation times among the recipe types using the means and sds. Additionally, it discusses the impact of different methods for calculating q1 and q3 on the identification of outliers.

Typology: Assignments

2019/2020

Uploaded on 01/31/2022

jeliyah-mohammadi
jeliyah-mohammadi 🇺🇸

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1. The code shows you how to create a subset of the data for recipe type C and then find the
mean and SD for the subset. Add code to get subsets for recipes A, B, and D. Report the
means and SDs for all four recipe types. Compare and contrast activation times among the
recipe types using the means and SDs.
●Recipe A mean: 486.25, SD: 79.6215
●Recipe B mean: 196.25, SD: 67.00435
●Recipe C mean: 656, SD: 74.09903
●Recipe D mean: 183.75, SD: 52.18157
●Out of these recipes, recipe C’s average time for the dough to rise is much higher
Than A,B, and D with recipe A being the second highest.
●The highest standard deviation for these recipes is recipe A. Which means recipe A has
more variability than the rest. The data for recipe A is more spread out than B,C, and D.
2. We mentioned that there are multiple methods to calculate Q1 and Q3. The default type in R
is type = 7. The type options go from 1 to 9 (don’t worry about understanding the
calculations; rather, we are only interested in if the differences impact our interpretations).
We show you the code to find Q1 and Q3 for the default type 7. Find the Q1/Q3 method that
matches your by-hand calculations for all the activation time data from HW3. What type is it
(give the number and the values of Q1 and Q3)?
●Type 2 and 5 matches my by-hand calculations. Q1 is 187.5 and Q3 is 564.5.
3. List the Q1 and Q3 values based on types 2, 3, and 7 (these are the types used in common
statistical software packages). Calculate the IQR for each of the three sets of numbers. Which
method covers the largest range of values in the IQR? Explain.
●Type 2
○Q1: 187.5
○Q3: 564.5
○IQR: 377
●Type 3
○Q1: 175
○Q3: 554
○IQR: 379
●Type 7
○Q1: 193.75
○Q3: 559.35
○IQR: 365.5
●Type 3 covers the largest range of values because it’s IQR is the largest compared to type 2 and 7.
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  1. The code shows you how to create a subset of the data for recipe type C and then find the mean and SD for the subset. Add code to get subsets for recipes A, B, and D. Report the means and SDs for all four recipe types. Compare and contrast activation times among the recipe types using the means and SDs. ● Recipe A mean: 486.25, SD: 79. ● Recipe B mean: 196.25, SD: 67. ● Recipe C mean: 656, SD: 74. ● Recipe D mean: 183.75, SD: 52. ● Out of these recipes, recipe C’s average time for the dough to rise is much higher Than A,B, and D with recipe A being the second highest. ● The highest standard deviation for these recipes is recipe A. Which means recipe A has more variability than the rest. The data for recipe A is more spread out than B,C, and D.
  2. We mentioned that there are multiple methods to calculate Q1 and Q3. The default type in R is type = 7. The type options go from 1 to 9 (don’t worry about understanding the calculations; rather, we are only interested in if the differences impact our interpretations). We show you the code to find Q1 and Q3 for the default type 7. Find the Q1/Q3 method that matches your by-hand calculations for all the activation time data from HW3. What type is it (give the number and the values of Q1 and Q3)? ● Type 2 and 5 matches my by-hand calculations. Q1 is 187.5 and Q3 is 564.5.
  3. List the Q1 and Q3 values based on types 2, 3, and 7 (these are the types used in common statistical software packages). Calculate the IQR for each of the three sets of numbers. Which method covers the largest range of values in the IQR? Explain. ● Type 2 ○ Q1: 187. ○ Q3: 564. ○ IQR: 377 ● Type 3 ○ Q1: 175 ○ Q3: 554 ○ IQR: 379 ● Type 7 ○ Q1: 193. ○ Q3: 559. ○ IQR: 365. ● Type 3 covers the largest range of values because it’s IQR is the largest compared to type 2 and 7.
  1. Would the differing values of 1.5(IQR) for types 2, 3, 7 change the flagging of outliers for any activation times? Show any calculations and explain. ● Type 2: 1.5* 377= 565. ○ Lower : 187.5-1.5377= - ○ Upper : 564.5+1.5377= 1130 ● Type 3: 1.5* 379= 568. ○ Lower : 175-1.5379= -393. ○ Upper : 554+ 1.5379= 1,122. ● Type 7: 1.5* 365.5= 548. ○ Lower : 193.75-1.5548.25= -628. ○ Upper : 559.25+1.5584.25= 1,435. ● No it would not change the flagging of outliers because there are still no numbers below the lower fences and none above the upper fence for these types.
  2. Create a fully labeled comparative boxplot for activation times by recipe type (you need to add the proper x - and y-axis labels to the code we provide). Save/export the comparative boxplot and include it as part of the answer to this problem. Then look at the histogram for all the data (should look like the one you included in HW3). Does the information in the comparative boxplot help you make sense of the pattern in the histogram (or change your description of the histogram from HW3)? Explain. ● The information in the comparative boxplot does help make sense of the pattern in the Histogram. Both of the histograms and box plot look alike, they are both skewed to the right and show the yeast activation time by recipes.