Relative Values
Which relative value divides a part by the whole, like services being 45 out of 100?
Structure (45%)
What is the simple mean of wages 4, 6 and 8 mln?
6 mln
Which mean is used for average growth rates?
The geometric mean
(Data for the first four clues: salaries 3, 4, 4, 5, 24)
What is the mean of these salaries?
8
(Data: 4, 6, 8, 10, 12, with mean = 8)
What is the range?
8 (12 − 4)
Services are 45 and industry is 35. What is the coordination value , to two decimals?
1.29
What is the formula for the simple mean?
x̄ = Σx ÷ n
Which mean is used for rates, such as speed, over equal distances?
The harmonic mean
(Data for the first four clues: salaries 3, 4, 4, 5, 24)
What is the median?
4
(Data: 4, 6, 8, 10, 12, with mean = 8)
The squared deviations sum to 40 and n = 5. What is the population variance?
8
Region A’s indicator is 12 and Region B’s is 8. What is the comparison value A ÷ B?
1.5
Which mean should you use when the groups differ in size?
The weighted mean, x̄ = Σ(x·f) ÷ Σf
What is the product of the growth coefficients 1.1, 1.2 and 1.3?
1.716
(Data for the first four clues: salaries 3, 4, 4, 5, 24)
What is the mode?
4
(Data: 4, 6, 8, 10, 12, with mean = 8)
What is the standard deviation, to two decimals?
2.83 (√8)
Which relative value is calculated as the current level ÷ the base level?
Dynamics
10 workers earn 4 mln, 10 earn 6 mln and 30 earn 8 mln. What is the weighted mean wage?
6.8 mln (340 ÷ 50)
You drive somewhere at 60 km/h and return at 40 km/h. What is your average speed?
48 km/h (2 ÷ (1/60 + 1/40))
(Data for the first four clues: salaries 3, 4, 4, 5, 24)
When mean > median > mode, what kind of skew does the data have?
Right skew
(Data: 4, 6, 8, 10, 12, with mean = 8)
What is the coefficient of variation (SD ÷ mean × 100)?
35.4%
GDP is 120 now and was 100 last year. By what percent did it grow?
20%
Why is the weighted mean (6.8) higher than the simple mean (6) in that example?
Because the largest group, 30 of the 50 workers, earns the highest wage (8 mln)
Growth was +10%, +20% and +30% over three years. What is the average annual growth?
About 19.7% (1.716^(1/3) ≈ 1.197)
Which is a better measure of the “typical” salary here, the mean or the median, and why?
The median (4), because the outlier 24 pulls the mean up to 8
(Data: 4, 6, 8, 10, 12, with mean = 8)
If you divide 40 by (n − 1) instead of n, what is the sample variance?
10