The document discusses the relationship between three types of averages - arithmetic mean (A.M.), geometric mean (G.M.), and harmonic mean (H.M.). It states that generally A.M. is greater than G.M., which is greater than H.M., and provides an example showing their calculation for numbers 2, 4, and 8. It also notes that if the numbers are equal, then all three averages will be equal, showing an example for numbers 4, 4, and 4. Finally, it summarizes that A.M. is greater than or equal to G.M., which is greater than or equal to H.M.

1. Relationship Among the
Averages
Dr. RMKV
SBKC

2. Relationship Among the Averages
• A.M > G.M. > H.M.
• E.g. 2,4,8 find AM,GM,HM
• AM =
2+4+8
3
=
14
3
= 4.67
• GM =
3
2𝑥 4 𝑥 8 =
3
64 = 4
• HM =
3
1
2
+
1
4
+
1
8
=
3
0.5+0.25+0.125
=
3
0.875
= 3.43

3. Relationship Among the Averages
• A.M = G.M. = H.M.
• E.g. 4,4,4 find AM,GM,HM
• AM =
4+4+4
3
=
12
3
= 4
• GM =
3
4𝑥 4 𝑥 4 =
3
64 = 4
• HM =
3
1
4
+
1
4
+
1
4
=
3
0.25+0.25+0.25
=
3
0.75
= 4

4. Relationship Among the Averages
• A.M > G.M. > H.M.
• A.M = G.M. = H.M.
• A.M ≥ G.M. ≥H.M.