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Chapter 4 Summarising Data
Recap and Outline Graphical methods of presenting data Numerical methods for summarising data Basic calculations MINITAB
Definitions Algebraic Notation 1st random sample 1 5 7 2nd random sample 2 0 3 typical random sample x 1 x 2 x 3 n summationdisplay i =1 x i = x 1 + x 2 + · · · + x n
Definitions Raising to powers: x k Ordering with brackets: × ÷ then + - 3 + 4 2 = 19 3 2 + 4 2 = 25 (3 + 4) 2 = 49 . In general summationdisplay x 2 negationslash = parenleftBig summationdisplay x parenrightBig 2
Measures of Location The Mean The Median The Mode
The Mean ( x ) x = 1 n n summationdisplay i =1 x i or x n
The Mean ( x ) Date Cars Sold Date Cars Sold 01/07/04 9 08/07/04 10 02/07/04 8 09/07/04 5 03/07/04 6 10/07/04 8 04/07/04 7 11/07/04 4 05/07/04 7 12/07/04 6 06/07/04 10 13/07/04 8 07/07/04 11 14/07/04 9 The mean number of cars sold per day is ¯ x = 9 + 8 + . . . + 8 + 9 14 = 7 . 71 .
The Mean ( x ) Cars Sold ( x ( j ) ) Frequency ( f j ) 4 1 5 1 6 2 7 2 8 3 9 2 10 2 11 1 Total ( n ) 14 The sample mean is x = 4 × 1 + 5 × 1 + 6 × 2 + . . . + 11 × 1 14 = 7 . 71 . In general x = 1 n k summationdisplay j =1 f j x ( j )
The Mean ( x ) Data: sample mean is 9.73 8.4 8.7 9.0 9.0 9.2 9.3 9.3 9.5 9.6 9.6 9.6 9.7 9.7 9.9 10.3 10.4 10.5 10.7 10.8 11.4 Class Interval Mid Point ( m j ) Frequency ( f j ) 8 . 0 x < 8 . 5 8.25 1 8 . 5 x < 9 . 0 8.75 1 9 . 0 x < 9 . 5 9.25 5 9 . 5 x < 10 . 0 9.75 7