Question: a) What kind of change do you see in the location of the data when tem

Question

Question:

a) What kind of change do you see in the location of the data when temperature of the process is increased? Use all the information necessary to support your description. (median, range, interquartile distance, etc.)

b) What kind of change do you see in the dispertion of the data when the temperature of the process is increased? Use all the information necessary to support your description (median, range, interquartile distance, etc.)

P3. (20 points) Consider the following data in a production process where a process temperature is set to a given value to then measure the total production time: Temperature (Celsius) Production time (seconds) 25 107 25 104 100 105 104 25 107 25 93 The Figure 1 shows the box plots of production time vs. each temperature in Celsius degrees. Boxplot of Production time (seconds) 108 106 104 8 102 100 y 96 92 90 Temperature (Celsius)

Explanation / Answer

For 25 degree celsius,

min = 92

max = 107

Median = 104

Q1 = 98

Q3 = 106

IQR = Q3 - Q1 = 106 - 98 = 8

For 50 degree celsius,

min = 92

max = 98

Median = 95

Q1 = 92

Q3 = 97

IQR = Q3 - Q1 = 97 - 92 = 5

(A) When the temperature increases, production time required decreases. As we can see in the above data median of the production time required for the temperature 25 degree celcius is 104 seconds where as for 50 degree celsius, it is 95 seconds.

(B)

For 25 degree celsius, interquartile range IQR = 8 and for 50 degree celsius, IQR = 5. This shows as temperature increased, time required for production is less dispersed. The same can be observed with minimum and maximum values of the respective data for two different tempratures.

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