## 14 Numerical Summary Of Data Slides Essay

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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 -...