Statistics

1. Explain following concepts:

Solution:

Distribution characteristics

a) Arithmetic mean:


b) Geometric mean:


c) Harmonic mean:


d) Mode mod(x) is the value that occurs the most frequently in a data set or a probability distribution.

e) Median med(x) is:

• the middle value of a data set sorted by the value containing odd number of elements
• aritmethmetic mean of the two middle values of a data set sorted by the value containing even number of elements

Variability characteristics

a) Range  

R = x_max - x_min

b) Variance (dispersion)


c) Standard deviation  

2. Following values were measured in the lab (in milimeters):
{302;310;312;310;313;318;305;309;310;309}

Solution:

Sorted values:
{302;305;309;309;310;310;310;312;313;318}

3.A car hit an average speed of v₁ = 20 kmph in the first half of the journey, and hit an average speed of v₂ = 80 kmph in the second half of the journey. Determine the average speed of the car.

Solution:

The car moved in different speeds, therefore it passed each half in different time.
The average speed equals to the harmonic mean of v₁ and v₂.



The average speed of the car was 32 kmph.

4.Following values were measured to determine the weight of a cog wheel. Find out the interval which contains the real weight value with a probability of 68%.

Solution:

5. Hounters A and B compete in target shooting. Who was more accurate and won the competition?

Solution:

Hunter A


Hunter B


Variance of hunter A equals s²(A) = 0,4 , variance of hunter B equals s²(B) = 3,6. Stands s²(A) < s²(B).
Hunter A won the competition.