Introduction to weighted arithmetic average:
Let us see about weighted arithmetic average. The weighted average is not anything but it’s similar as that of arithmetic average, where as every of the data is donated uniformly with the weighed value. If each the weighted values are identical, then the weighed average is similar to the arithmetic average. The weighted average essentially performs similar fashion to the arithmetic average. The expression weighted average can also be named as weighted arithmetic average or weighted harmonic average. I like to share this What Does Arithmetic Mean with you all through my article.
Formula for Weighted Arithmetic Average:
The weighted average is described as the addition of the experiential values multiplied with the allocated weights which is separated by the addition of the observed values.
Formula of weighted average is defined by,
` barx_w = (sum_(i=1)^n (w_i* x_i) )/ (sum_(i=1)^n (w_i)).`
Description:
`barx_w` is the weighted average variable
`w_i ` is the allocated weighted value
`x_i` is the observed values. Is this topic how to solve a math problem step by step hard for you? Watch out for my coming posts.
Examples of Weighted Arithmetic Average:
Let us see about the weighted arithmetic average problems.
Example 1:
Find the weighted average from the experiential values 25, 30, 35, 40 and the allocated weights are 20, 30, 40, 50.
Solution:
The given `barx_i` = 25, 30, 35, 40
The given ` w_i` = 20, 30, 40,50.
Formula of weighted average is,
`barx_w = (sum_(i=1)^n (w_i* x_i))/ (sum_(i=1)^n (w_i)).`
= `((20 * 25) +(30*30)+(40*35)+(50*40)) / (20+30+40+50)` .
= `4800 / 140` .
= 34.2857143
Example 2:
Find weighted average from the experiential values 65, 70, 85, 90 and the allocated weights are 60, 70, 80, 90.
Solution:
The given` barx_i` = 65, 80, 85, 90
The given `w_i` = 60, 70, 80, 90
Formula of weighted average is,
`barx_w = (sum_(i=1)^n (w_i* x_i)) / (sum_(i=1)^n (w_i)).`
= `((65*60) + (80*70) + (85*80) + (90 * 90)) / (60+70+80+90)` .
= `24400 / 300` .
= 81.3333333
Example 3:
Find weighted average from the experiential values 5, 10, 15, 20 and the allocated weights are 20, 30, 40, 50.
Solution:
The given `barx_i ` = 5, 10, 15, 20
The given `w_i` = 20, 30, 40, 50.
Formula of weighted average is,
`barx_w = (sum_(i=1)^n (w_i* x_i)) / (sum_(i=1)^n (w_i))`
=`((20 * 5) + (30 * 10) + (40 * 15)) / (20+30+40+50).`
=` 2000 /140.`
`barx_w = 14.2857143. `
Let us see about weighted arithmetic average. The weighted average is not anything but it’s similar as that of arithmetic average, where as every of the data is donated uniformly with the weighed value. If each the weighted values are identical, then the weighed average is similar to the arithmetic average. The weighted average essentially performs similar fashion to the arithmetic average. The expression weighted average can also be named as weighted arithmetic average or weighted harmonic average. I like to share this What Does Arithmetic Mean with you all through my article.
Formula for Weighted Arithmetic Average:
The weighted average is described as the addition of the experiential values multiplied with the allocated weights which is separated by the addition of the observed values.
Formula of weighted average is defined by,
` barx_w = (sum_(i=1)^n (w_i* x_i) )/ (sum_(i=1)^n (w_i)).`
Description:
`barx_w` is the weighted average variable
`w_i ` is the allocated weighted value
`x_i` is the observed values. Is this topic how to solve a math problem step by step hard for you? Watch out for my coming posts.
Examples of Weighted Arithmetic Average:
Let us see about the weighted arithmetic average problems.
Example 1:
Find the weighted average from the experiential values 25, 30, 35, 40 and the allocated weights are 20, 30, 40, 50.
Solution:
The given `barx_i` = 25, 30, 35, 40
The given ` w_i` = 20, 30, 40,50.
Formula of weighted average is,
`barx_w = (sum_(i=1)^n (w_i* x_i))/ (sum_(i=1)^n (w_i)).`
= `((20 * 25) +(30*30)+(40*35)+(50*40)) / (20+30+40+50)` .
= `4800 / 140` .
= 34.2857143
Example 2:
Find weighted average from the experiential values 65, 70, 85, 90 and the allocated weights are 60, 70, 80, 90.
Solution:
The given` barx_i` = 65, 80, 85, 90
The given `w_i` = 60, 70, 80, 90
Formula of weighted average is,
`barx_w = (sum_(i=1)^n (w_i* x_i)) / (sum_(i=1)^n (w_i)).`
= `((65*60) + (80*70) + (85*80) + (90 * 90)) / (60+70+80+90)` .
= `24400 / 300` .
= 81.3333333
Example 3:
Find weighted average from the experiential values 5, 10, 15, 20 and the allocated weights are 20, 30, 40, 50.
Solution:
The given `barx_i ` = 5, 10, 15, 20
The given `w_i` = 20, 30, 40, 50.
Formula of weighted average is,
`barx_w = (sum_(i=1)^n (w_i* x_i)) / (sum_(i=1)^n (w_i))`
=`((20 * 5) + (30 * 10) + (40 * 15)) / (20+30+40+50).`
=` 2000 /140.`
`barx_w = 14.2857143. `
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