Home > Statistical Methods calculators > Arithmetic Mean, Geometric Mean, Harmonic Mean calculator









Solution 


Share with Your Friends :

Arithmetic mean, Geometric mean, Harmonic mean

1. Find Arithmetic mean, Geometric mean, Harmonic mean for ungrouped data like 2,3,4,5,6
2. Find X where Arithmetic mean(AM)=3.5 for ungrouped data 2,3,X,5
3. Find Mode when Mean=3 and Median=4

1. Find Arithmetic mean(AM), Geometric mean(GM), Harmonic mean(HM)

1. Find Arithematic mean for data `2,3,4,5,6`
AM `= ( X_1 + X_2 + X_3 + X_4 + X_5 )/5`
AM `= ( 2 + 3 + 4 + 5 + 6 )/5`
AM `= 20/5`
AM `= 4`
2. Find Geometric mean for data `2,3,4,5,6`
GM `= root (5)( X_1 × X_2 × X_3 × X_4 × X_5 )`
GM `= root (5)( 2 × 3 × 4 × 5 × 6 )`
GM `= root (5)(720)`
GM `= 3.7279`
3. Find Harmonic mean for data `2,3,4,5,6`
HM `= N/( 1/X_1 + 1/X_2 + 1/X_3 + 1/X_4 + 1/X_5 )`
HM = `5/( 1/2 + 1/3 + 1/4 + 1/5 + 1/6 )`
After solving, we get HM `= 3.4483`

2. Find X from Arithmetic mean(AM), Geometric mean(GM), Harmonic mean(HM)

1. Find value of `X` where Arithmetic mean `= 3.5` for data `2,3,X,5`
AM `= ( 2 + 3 + X + 5 )/4`
`3.5 = ( 2 + 3 + X + 5 )/4`
`3.5 × 4 = 10 + X`
`X = 14  10`
`X = 4`

3. Find Mean or Median or Mode from other two's

1. Find Mode when Mean=3 and Median=4
We have given Mean (`bar X`) `= 3`, Median(`M`) `= 4`, Mode(`Z`) `= ?`
`Z = 3 M  2 bar X`
`Z = 3 * 4  2 * 3`
`Z = 12  6`
`Z = 6`
2. Find Median when Mean=5 and Mode=11
We have given Mean(`bar X`) `= 5`, Mode(`Z`) `= 11`, Median(`M`) `= ?`
`Z = 3 M  2 bar X`
`3 M = Z + 2 bar X`
`3 M = 11 + 2 * 5`
`3 M = 11 + 10`
`M = 21/3`
`M = 7`







