Information

Central tendency measures


There are several measures of central tendency, however in this material we will study only those that are most significant for the theory of market research.

The most important measures of central tendency are the arithmetic mean, arithmetic mean for pooled data, weighted arithmetic mean, median, mode, geometric mean, harmonic mean, quartiles.

When studying variability, the most important measures are: amplitude, standard deviation and variance.

Measures

Formula

Example

Arithmetic average

Arithmetic mean for grouped data

Weighted Arithmetic Average

4 (4) + 6 (9) = 7

Median

1) If n is odd, the value is central, 2) if n is even, the value is the average of the two central values.

12 13 14 = 13 12 13 14 15 = 13,5

Fashion

Value that occurs most often.

22 23 22 22 34 45 = 22

Geometric mean

G = nov X1 X2

3v12 x 14 x 16 = 13.90

Harmonic Average

Quartiles

Quartile Calculation Example:

For the sample below, calculate the first and third quartiles:

1) Values ​​in ascending order and calculation of p (i).

13,3 13,5 17,2 13,8 12,3 12,7 13,0 14,5 14,9 15,8 13,1 13,3 14,1

12,3 12,7 13,0 13,1 13,3 13,3 13,5 13,8 14,1 14,5 14,9 15,8 17,2

X (i) i

12,3

12,7

13,0

13,1

13,3

13,3

13,5

13,8

14,1

14,5

14,9

15,8

17,2

01

02

03

04

05

06

07

08

09

10

11

12

13

0,038

0,115

0,192

0,269

0,346

0,423

0,500

0,577

0,654

0,731

0,808

0,885

0,962

2) Values ​​immediately above and below 0.25 (13.0 and 13.1), associated with p(inf) = 0.192 and p (sup) = 0,269

Values ​​immediately above and below 0.75: x(inf) = 14.5 and x (sup) = 14.9, associated with p(inf) = 0.731 and p(sup) = 0,808:

The value for the second quartile is represented by the median (13.5). Next: Variability