### Essay preview

Numerical summary of data

Covariance and Correlation

Numerical Summary of Data

Pan Chao

November 17, 2014

Numerical summary of data

Covariance and Correlation

Measures of center

Measures of Center

1. Mean: arithmetic average

x1 + x2 + . . . + xn

1∑

=

xi

n

n

n

x

¯=

i=1

Example:

1, 2, 2, 3, 4, 7, 9

x

¯=

1+2+2+3+4+7+9

= 4.

7

Numerical summary of data

Covariance and Correlation

Measures of center

2. Mode: most frequent value in a data set, highest peak.

Example: 2 is the mode in the previous example.

Remark: can have more than one modes.

Numerical summary of data

Covariance and Correlation

Measures of center

3. Median: midpoint of the data such that half of the values are smaller and half of the values are larger.

How to find the median:

1. arrange the data in increasing order (from smallest to largest) 2. count the number of observations, n.

3a. If n is odd, median is the middle ordered value:

(

M=

n+1

2

)th

ordered value

3b. If n is even, median is the average of the two middle ordered values:

(n

)th

( n )th

and

+1

ordered value

M = average of

2

2

Example : observations 7, 9, 10, 12, 14 (The sample median is 10) Example : observations 3, 4, 9, 12, 14, 19 (The sample median is 10.5)

Numerical summary of data

Covariance and Correlation

Measures of center

Example

Bob’s last 20 golf scores, beginning with his last score

69

76

77

76

73

75

81

83

77

77

82

77

77

78

75

80

80

78

79

84

1. What is the mode for this data set?

69, 73, 75, 75, 76, 76, 77, 77, 77, 77, 77,

78, 78, 79, 80, 80, 81, 82, 83, 84

2. Determine the median (77)

3. Calculate Bob’s mean golf score (77.7)

Numerical summary of data

Measures of variability

Measures of Variability

1. Range: = max -...

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