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 = ^{no}v X_{1 }X_{2}… | ^{3}v12 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