Question

In: Statistics and Probability

The following table provides data for 20 samples each of size five. Sample x1 x2 x3...

  1. The following table provides data for 20 samples each of size five.

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
  1. Identify out-of-control points. If necessary, recompute the control limits after removing the outliers. What do you conclude? (10 pts) Please answer in detail using excel

Solutions

Expert Solution

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.

orchestra answered 1 year ago
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