The mean of discrete observations \[{y_1},{y_2},.....,{y_n}\] is given by
A. \[\dfrac{{\sum\limits_{i = 1}^n {{y_i}} }}{n}\]
B. \[\dfrac{{\sum\limits_{i = 1}^n {{y_i}} }}{{\sum\limits_{i = 1}^n i }}\]
C. \[\dfrac{{\sum\limits_{i = 1}^n {{y_i}{f_i}} }}{n}\]
D. \[\dfrac{{\sum\limits_{i = 1}^n {{y_i}{f_i}} }}{{\sum\limits_{i = 1}^n {{f_i}} }}\]
Answer
Verified
144.6k+ views
- Hint: Discrete observations means the observations are distinct. There is a clear gap between the observations. Mean is a measure of the central tendency of a finite set of observations. It is also known as average. The average of some observations is obtained by dividing the sum of the observations by the total number of observations.
Formula used:
\[\text{ Mean of the observations} =\dfrac{\text{ (sum of the observations)}}{\text{(number of observations)}}\]
Complete step-by-step solution:
Here the observations are \[{y_1},{y_2},.....,{y_n}\]
Sum of the observations is \[{y_1} + {y_2} + ..... + {y_n}\], which can be expressed as the summation \[\sum\limits_{i = 1}^n {{y_i}} \], where \[i = 1,2,.....,n\]
and number of observations is \[n\].
Now, using the formula of mean, we get
\[m = \dfrac{{\sum\limits_{i = 1}^n {{y_i}} }}{n}\]
So, option A is correct.
Additional information:
The mean is the same as the average of the data. The sum of all observations divided by the number of observations is the mean of the data.
Discrete observation: If there is a separation between two observations, then data is known as discrete observations.
Note: \[\sum\limits_{i = 1}^n {{y_i}} \]represents the sum of the observations \[{y_1},{y_2},.....,{y_n}\], where \[i = 1,2,.....,n\]. You must have to write the starting value of \[i\] under the summation symbol \[\sum {} \]and the end value of \[i\] above the summation symbol. Since the value of \[i\] starts from \[1\] and ends at \[n\], so the number of values of \[i\] is equal to \[n\] and hence number of observations is \[n\].
Formula used:
\[\text{ Mean of the observations} =\dfrac{\text{ (sum of the observations)}}{\text{(number of observations)}}\]
Complete step-by-step solution:
Here the observations are \[{y_1},{y_2},.....,{y_n}\]
Sum of the observations is \[{y_1} + {y_2} + ..... + {y_n}\], which can be expressed as the summation \[\sum\limits_{i = 1}^n {{y_i}} \], where \[i = 1,2,.....,n\]
and number of observations is \[n\].
Now, using the formula of mean, we get
\[m = \dfrac{{\sum\limits_{i = 1}^n {{y_i}} }}{n}\]
So, option A is correct.
Additional information:
The mean is the same as the average of the data. The sum of all observations divided by the number of observations is the mean of the data.
Discrete observation: If there is a separation between two observations, then data is known as discrete observations.
Note: \[\sum\limits_{i = 1}^n {{y_i}} \]represents the sum of the observations \[{y_1},{y_2},.....,{y_n}\], where \[i = 1,2,.....,n\]. You must have to write the starting value of \[i\] under the summation symbol \[\sum {} \]and the end value of \[i\] above the summation symbol. Since the value of \[i\] starts from \[1\] and ends at \[n\], so the number of values of \[i\] is equal to \[n\] and hence number of observations is \[n\].
Recently Updated Pages
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Find the values of other five trigonometric ratios class 10 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Change the following sentences into negative and interrogative class 10 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the past tense of read class 10 english CBSE
What is the difference between anaerobic aerobic respiration class 10 biology CBSE
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Discuss the main reasons for poverty in India
What is the past participle of wear Is it worn or class 10 english CBSE
Formula for number of images formed by two plane mirrors class 12 physics JEE_Main