Please solve the screenshot! Please show all work. A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information.median = 201.3lower fourth = 198.0upper fourth = 216.2Three smallest observations125.8 188.3 194.4Three largest observations221.6 231.1 251.1(a) Are there any outliers in the sample?O YesO NoAny extreme outliers?O YesO No

Name: Please solve the screenshot! Please show all work. A sample of 20 glas
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please solve the screenshot! Please show all work. A sample of 20 glass bottles of a particular type was selected, and the internal pressure strength of each bottle was determined. Consider the following partial sample information.median = 201.3lower

Total number of glass bottle is 20. Median of internal pressure is 201.3. Lower fourth of internal pressure is 198.0. Upper fourth of internal pressure is 216.2. Three smallest observation of internal pressure is 125.8,188.3,194.4. Three largest observation of internal pressure is 221.6,231.1,251.1.Consider, total number of observation of the internal pressure of the glass bottle is n. When the total number of observation is arranged from smallest to largest and divided that sequence into two halves then median of smallest part half is called lower fourth and the median of the largest part half is called upper fourth. If there are total number of observation is odd number then median of whole is observation is added with smaller part half and also with larger part half. The difference in median of lower and upper forth is called fourth spread fs. fs=upper fourth - lower fourth =216.2-198.0 =18.2 The observation which are bigger than the 1.5fs from the lower and upper fourth are called outlier. When the outlier is bigger than 3fs from the nearest forth then it is called extreme outlier otherwise it called mild outlier. Checking for the outlier, 1.5fs=1.5×18.2=27.3 3fs=3×18.2=54.6 Using this we can calculate the limits for the extreme and mild outlier. Taking x~1 as upper fourth and x~2as lower fourth. For mild outlier, x~1+1.5fs=216.2+27.3=243.5x~2-1.5fs=198.0-27.3=170.7 For extreme outlier, x~1+3fs=216.2+54.6=270.8x~2-3fs=198.0-54.6=143.4 The values between 143.4 to 170.7 and the values between 243.5 to 270.8 is called Mild outlier. The extreme outlier are all values which are smaller than 143.4 and bigger than 270.8. a) Yes, both types of outlier in the sample. b)In the observation 125.8 is smaller than the 143.4 is called the extreme outlier from the lower fourth. About the upper forth there is no value which is bigger than 270.8. hence there is one extreme outlier.