subject: Introduction To Sample Statistics Exam: [print this page] Statistics is defined as the branch of mathematics which studies methods for the calculation of probabilities. Statistics done normally with data collected for specific purposes. Normally we make decisions about the data by analyzing and interpreting it. The process used for finding a representative value for the given data are called the measure of central tendency. The three measures of central tendency were Arithmetic Mean, also median and mode. Let us take sample statistics exam.
Sample Problems for Statistics Exam:
Ex 1: Find the mean of every prime numbers less than 20.
Sol: The prime numbers less than 20 are 2,3,5,7,11,13,17and19
Total number of observations: 8
Mean = Sum of every prime numbers/Total Number of observations
= (2+3+ 5+7+11+13+17+19)/8
= 77/8
= 9.625
So, the mean of all prime numbers less than 20 = 9.625
Ex 2: Find the Median of the scores 72,28,40,46,64,54.
Sol:First arrange in ascending order. That is 28,40,46,54,64,and72
The Median is '(46+54)/(2)' ='(100)/(2)' = 50
Median of volley ball team= 50
Ex 3:Find the median of the scores 72,26,84,62,48
First we arrange the values in ascending order. that is 26,48,62,72,84
Ex 4:Find the mean deviation of the median for the following data:
3,9,5,3,12,10,18,4,7,19,21.
Sol: Here the number of observations is 11 which is odd. Arranging the data into
ascending order, we have 3,3,4,5,7,9,10,12,18,19,21
Now Median =('(11+1)/(2)' ) or 6th observation = 9
Ex 5: The points scored by a volley ball team in ten matches are:
34,42,31,37,53,56,56,51,105 and 69
Find the mode:
Sol: First arrange the given scores in ascending order
31,34,37,42,51,53,56,56,69,105
56 is repeated maximum number of times ( twice)
Hence, the mode = 56
Sample Exam of Statisitics
1) Find the mean of the numbers, 75,65,70,72,73,78.
Answer: 72.16
2) Find the mean for the numbers 7,9,5,3,15,15.
Answer: = 9
3) Find the mean for the numbers 8,10,6,4,16,16.
Answer: = 10
4) Find the median of the following numbers 110,95,90,85,100,105,80.
Answer: 95
5) Find the median of the following numbers 70,82,78,76,74,80,72.
Answer: 76
6) Find the mode of 12,12,11,10,10,10,9,8.
Answer: 10
7) Find the mode of the numbers,25,26,27,27,28,29,30.
Answer: 27
8) Find the mode of the numbers,25,26,29,29,28,29,30.
Answer: 29
Introduction to frequency table examples:
Frequency is the digit of occurrence of a repeat the event per unit time it is also called temporal frequency. The time period of one cycle in a repeat the event, so the period is the the same of the frequency.
Frequency of waves
Frequency is inverse of the concept of wavelength, simply, frequency is inversely proportional to wavelength . The frequency f is the same to the phase velocity v of the wave divided by the wavelength of the wave:
f=v/, then v=c f=c/
Other Types of Frequency Table Examples:
The Angular frequency is define the rate of alteration in the orientation slant, or in the phase of a sinusoidal waveform
Angular frequency is considered in radians per second (rad/s).
The frequency is analogous to sequential frequency, but the time axis is replace the one or more spatial displacement axis.
