In: Statistics and Probability
Sample |
x1 |
x2 |
x3 |
x4 |
x5 |
1 |
4.960 |
4.946 |
4.950 |
4.956 |
4.958 |
2 |
4.958 |
4.927 |
4.935 |
4.940 |
4.950 |
3 |
4.971 |
4.929 |
4.965 |
4.952 |
4.938 |
4 |
4.940 |
4.982 |
4.970 |
4.953 |
4.960 |
5 |
4.964 |
4.950 |
4.953 |
4.962 |
4.956 |
6 |
4.969 |
4.951 |
4.955 |
4.966 |
4.954 |
7 |
4.960 |
4.944 |
4.957 |
4.948 |
4.951 |
8 |
4.969 |
4.949 |
4.963 |
4.952 |
4.962 |
9 |
4.984 |
4.928 |
4.960 |
4.943 |
4.955 |
10 |
4.970 |
4.934 |
4.961 |
4.940 |
4.965 |
11 |
4.975 |
4.959 |
4.962 |
4.971 |
4.968 |
12 |
4.945 |
4.977 |
4.950 |
4.969 |
4.954 |
13 |
4.976 |
4.964 |
4.970 |
4.968 |
4.972 |
14 |
4.970 |
4.954 |
4.964 |
4.959 |
4.968 |
15 |
4.982 |
4.962 |
4.968 |
4.975 |
4.963 |
16 |
4.961 |
4.943 |
4.950 |
4.949 |
4.957 |
17 |
4.980 |
4.970 |
4.975 |
4.978 |
4.977 |
18 |
4.975 |
4.968 |
4.971 |
4.969 |
4.972 |
19 |
4.977 |
4.966 |
4.969 |
4.973 |
4.970 |
20 |
4.975 |
4.967 |
4.969 |
4.972 |
4.972 |
Answer :
1) We have to obtain outliers
By using Excel
Functions :
1. Quartiles =QUARTILE()
2. Interquartile Range = Q3 - Q1
3. Lower limit = Q1 - ( 1.5 * Interquartile Range)
4. Upper limit = Q3 + ( 1.5 * Interquartile Range)
Sample | x1 | x2 | x3 | x4 | x5 | |
1 | 4.96 | 4.946 | 4.95 | 4.956 | 4.958 | |
2 | 4.958 | 4.927 | 4.935 | 4.94 | 4.95 | |
3 | 4.971 | 4.929 | 4.965 | 4.952 | 4.938 | |
4 | 4.94 | 4.982 | 4.97 | 4.953 | 4.96 | |
5 | 4.964 | 4.95 | 4.953 | 4.962 | 4.956 | |
6 | 4.969 | 4.951 | 4.955 | 4.966 | 4.954 | |
7 | 4.96 | 4.944 | 4.957 | 4.948 | 4.951 | |
8 | 4.969 | 4.949 | 4.963 | 4.952 | 4.962 | |
9 | 4.984 | 4.928 | 4.96 | 4.943 | 4.955 | |
10 | 4.97 | 4.934 | 4.961 | 4.94 | 4.965 | |
11 | 4.975 | 4.959 | 4.962 | 4.971 | 4.968 | |
12 | 4.945 | 4.977 | 4.95 | 4.969 | 4.954 | |
13 | 4.976 | 4.964 | 4.97 | 4.968 | 4.972 | |
14 | 4.97 | 4.954 | 4.964 | 4.959 | 4.968 | |
15 | 4.982 | 4.962 | 4.968 | 4.975 | 4.963 | |
16 | 4.961 | 4.943 | 4.95 | 4.949 | 4.957 | |
17 | 4.98 | 4.97 | 4.975 | 4.978 | 4.977 | |
Q1 | 4.96 | 4.943 | 4.953 | 4.949 | 4.954 | |
Q3 | 4.975 | 4.962 | 4.965 | 4.968 | 4.965 | |
IQR | 0.015 | 0.019 | 0.012 | 0.019 | 0.011 | |
Lower limit | 4.9375 | 4.9145 | 4.935 | 4.9205 | 4.9375 | |
Upper limit | 4.9975 | 4.9905 | 4.983 | 4.9965 |
4.9815 |
To Identify the Outliers:
OR function is used to Identify the Outliers.
TRUE value indicates an outlier
Hence ,
outlier x1 | outlier x2 | outlier x3 | outlier x4 | outlier x5 |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
FALSE | FALSE | FALSE | FALSE | FALSE |
Hence, Given data is Under Control.