What is the next term in the below given senes?
CEG, FHJ, IKM, LNP, (?)
OQS
MOS
ORT
OPR
Answers
Answer:
OQS
Step-by-step explanation:
ASSUME : CEF,GHI,JKL,MNO,PQR,STU,VWX,YZ
ALTERING : CEG,FHJ,IKM,LNP,OQS,RTV,UWY,XYZ.
RIGHT ANSWER : OQS.
BECAUSE IN THREE LETTERS CENTER LETTER IS CONSTANT, THE FIRST & LAST LETTER ONLY CHANGING
Answer:
OQS
Step-by-step explanation:
This article is about the mathematical concept. For other uses, see Mean (disambiguation). For the state of being mean or cruel, see Meanness. For broader coverage of this topic,
This article's lead section may be too short to adequately summarize the key points. Please consider expanding the lead to provide an accessible overview of all important aspects of the article. (October 2021)
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set.
For a data set, the arithmetic mean, also known as "arithmetic average", is a measure of central tendency of a finite set of numbers: specifically, the sum of the values divided by the number of values. The arithmetic mean of a set of numbers x1, x2, ..., xn is typically denoted using an overhead bar,
If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the sample mean ( to distinguish it from the mean, or expected value, of the underlying distribution, the population mean
Arithmetic mean (AM)
The arithmetic mean (or simply mean) of a list of numbers, is the sum of all of the numbers divided by the number of numbers. Similarly, the mean of a sample
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1
,
�
2
,
…
,
�
�
x_{1},x_{2},\ldots ,x_{n}, usually denoted by
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¯{\bar {x}}, is the sum of the sampled values divided by the number of items in the sample.
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¯
=
1
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(
∑
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=
1
�
�
�
)
=
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1
+
�
2
+
⋯
+
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�
�
{\displaystyle {\bar {x}}={\frac {1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)={\frac {x_{1}+x_{2}+\cdots +x_{n}}{n}}}
For example, the arithmetic mean of five values: 4, 36, 45, 50, 75 is:
4
+
36
+
45
+
50
+
75
5
=
210
5
=
42.
{\displaystyle {\frac {4+36+45+50+75}{5}}={\frac {210}{5}}=42.}
Geometric mean (GM)
The geometric mean is an average that is useful for sets of positive numbers, that are interpreted according to their product (as is the case with rates of growth) and not their sum (as is the case with the arithmetic mean):
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¯
=
(
∏
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=
1
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)
1
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=
(
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1
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2
⋯
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)
1
�
{\displaystyle {\bar {x}}=\left(\prod _{i=1}^{n}{x_{i}}\right)^{\frac {1}{n}}=\left(x_{1}x_{2}\cdots x_{n}\right)^{\frac {1}{n}}} [2]
For example, the geometric mean of five values: 4, 36, 45, 50, 75 is:
(
4
×
36
×
45
×
50
×
75
)
1
5
=
24
300
000
5
=
30.
{\displaystyle (4\times 36\times 45\times 50\times 75)^{\frac {1}{5}}={\sqrt[{5}]{24\;300\;000}}=30.}
Harmonic mean (HM)
The harmonic mean is an average which is useful for sets of numbers which are defined in relation to some unit, as in the case of speed (i.e., distance per unit of time):
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¯
=
�
(
∑
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=
1
�
1
�
�
)
−
1
{\displaystyle {\bar {x}}=n\left(\sum _{i=1}^{n}{\frac {1}{x_{i}}}\right)^{-1}}
For example, the harmonic mean of the five values: 4, 36, 45, 50, 75 is
5
1
4
+
1
36
+
1
45
+
1
50
+
1
75
=
5
1
3
=
15.
{\frac {5}{{\tfrac {1}{4}}+{\tfrac {1}{36}}+{\tfrac {1}{45}}+{\tfrac {1}{50}}+{\tfrac {1}{75}}}}={\frac {5}{\;{\tfrac {1}{3}}\;}}=15.
Relationship between AM, GM, and HM
Proof without words of the inequality of arithmetic and geometric means:
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�
PR is the diameter of a circle centered on
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O; its radius
�
�
AO is the arithmetic mean of
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a and
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b. Using the geometric mean theorem, triangle
�
�
�
{\displaystyle PGR}'s altitude
�
�
{\displaystyle GQ} is the geometric mean. For any ratio
�
:
�
{\displaystyle a:b},
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�
≥
�
�
{\displaystyle AO\geq GQ}.
Main article: Inequality of arithmetic and geometric means
AM, GM, and HM satisfy these inequalities:
A
M
≥
G
M
≥
H
M
{\displaystyle \mathrm {AM} \geq \mathrm {GM} \geq \mathrm {HM} \,}
Equality holds if all the elements of the given sample are equal.
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