MEASURE OF CENTRAL TENDENCY

INTRODUCTION

MEASURES OF CENTRAL TENDENCY

• THE MEASURE OF CENTRAL TENDENCY :

As the name implies, refer to some typical central values Distribution;

There are five such measures given below:

1. The Arithmetic Mean
2. The Median
3. The Mode
4. The Geometric Mean
5. The Harmonic Mean

• The Arithmetic Mean:

The arithmetic mean is algebraically defines “As the sum of all the observations or measures divided by their number”

The mean of a sample or a population is computed by adding all of the observations and dividing by the of

Observations. Returning to the example of the five women, the mean weight would equal

(100 + 100 + 130 + 140 + 150)/5 = 620/5 = 124 pounds.

• Geometric Mean:

Technically defined as "the 'n'th root product of 'n' numbers", the formula for calculating geometric mean is most easily written as:

Harmonic Mean:

The harmonic mean is define as “the reciprocal of the arithmetic mean of the reciprocals”

Harmonic Mean Definition:
Harmonic mean is used to calculate the average of a set of numbers. Here the number of elements will be averaged and divided by the sum of the reciprocals of the elements. Harmonic mean is always the lowest mean.

FORMULAS TO CALCULATE THE CENTRAL TENDENCY:

• Arithmetic Mean:

For Un Group Data:

X = ∑X/n

For Un Group Data;

X = ∑ƒ/∑ƒ

• Geometric Mean:

For Group Data:

log G.M =∑log x/n

For Un Group Data:

log G.M =∑ƒ.log x/n

Harmonic Mean:

For Un Group Data:

H.M = n/∑ (1/x)

Or 1/H.M = n/∑ (1/x)

For Group Data:

H.M = n/∑ (ƒ/x)

Table: LABOUR FORCE PARTICIPATION RATES FOR MALE AND FEMALE:

C - I	F	C - B	X	FX	F	FX
10 - 14	7	9.5 - 14.5	12	84	2	24
15 - 19	41	14.5 – 19.5	17	697	8	136
20 - 24	79	19.5 – 24.5	22	1738	15	330
25 - 29	96	24.5 – 29.5	27	2592	12	324
30 - 34	98	29.5 - 34.5	32	3136	11	352
35 - 39	98	34.5 - 39.5	37	3626	14	518
40 - 44	98	39.5 – 44.5	42	4116	12	504
45 - 49	97	44.5 -49.5	47	4559	11	517
50 - 54	95	49.5 – 54.5	52	4940	10	520
55 - 59	91	54.5 - 59.5	57	5187	9	513
60 - 64	61	59.5 – 64.5	62	3782	5	310
65 - 69	33	64.5 – 69.5	67	2211	6	402
SUM	894			36668	115	4450

Calculation of Arithmetic Mean:

For Mal :

X = ∑FX/∑F

X = 36668/894

X = 41.01

For Female:

X = ∑FX/∑X

X = 4450 /115

X = 38.69

Table: 2 LABOUR FORCE PARTICIPATION RATES:

C - I	F	X	Log X	f(log x)	F	f(log x)
10 - 14	7	12	1.079	7.553	2	2.158
15 - 19	41	17	1.230	50.43	8	9.84
20 - 24	79	22	1.342	106.018	15	20.13
25 - 29	96	27	1.431	137.376	12	17.172
30 - 34	98	32	1.505	147.49	11	16.55
35 - 39	98	37	1.568	153.664	14	21.95
40 - 44	98	42	1.623	159.054	12	19.476
45 - 49	97	47	1.672	162.184	11	18.392
50 - 54	95	52	1.716	163.02	10	17.16
55 - 59	91	57	1.755	159.705	9	15.795
60 - 64	61	62	1.792	109.312	5	8.96
65 - 69	33	67	1.826	60.258	6	10.956
SUM	894			1416.064	115	178.546

Calculation Of Geometric Mean:

For Male:

log G.M=∑ƒ (log x)/n

log G.M= 1416.064/894

log G.M=1.583

G.M = Anti log = 38.23

For Female:

Log G.M = 178.546/115

Log G.M = 1.552

G.M = Anti log =35.645

Table: LABOUR FOURCE PARTICIPATION:

C - I	F	X	F/X	F	F/X
10 - 14	7	12	0.5833	2	0.166
15 -19	41	17	2.4117	8	0.470
20 - 24	79	22	3.5909	15	0.6818
25 - 29	96	27	305555	12	0.4444
30 - 34	98	32	3.0625	11	0.3437
35 - 39	98	37	2.6486	14	0.3783
40 - 44	98	42	2.3333	12	0.285
45 - 49	97	47	2.063	11	0.234
50 - 54	95	52	1.8269	10	0.192
55 - 59	91	57	1.5964	9	0.157
60 - 64	61	62	0.9838	5	0.080
65 - 69	33	67	0.4925	6	0.089
SUM	894			115

Calculation of Harmonic Mean:

For Male;

H.M = n/∑ (ƒ/x)

H.M = 894/25.5484

H.M = 34.992

For Female: H.M = 115/3.4575

H.M = 33.26

Table No: 4 TOTAL OF LABOUR FOURCE AND UN EMPLOYED RATES

C - I	F	C - B	X	FX	Log x	∑ƒ(log x)	f/x
10 - 14	4.96	9.5 - 14.5	12	59.52	1.079	5.3518	0.413
15 - 19	25.9	14.5 - 19.5	17	440.3	1.230	31.857	1.523
20 - 24	48.94	19.5 - 24.5	22	1076.68	1.342	65.677	2.224
25 - 29	54.12	24.5 - 29.5	27	1461.24	1.431	77.445	2.004
30 - 34	53.83	29.5 - 34.5	32	1722.56	1.505	81.014	1.682
35 - 39	56.1	34.5 - 39.5	37	2075.7	1.568	87.964	1.516
40 - 44	55.86	39.5 - 44.5	42	2346.12	1.623	90.66	1.33
45 - 49	56.61	44.5 - 49.5	47	2660.67	1.672	94.651	1.204
50 - 54	58.02	49.5 - 54.5	52	3017.04	1.716	99.56	1.115
55 - 59	53.31	54.5 - 59.5	57	3038.67	1.755	93.55	0.935
60 - 64	36.1	59.5 - 64.5	62	2238.2	1.792	64.69	0.582
65 - 69	22.2	64.5 -69.5	67	1487.4	1.826	40.537	0.331
	525.95s			21624.1		832.956	14.859

Calculation of Arithmetic Mean For Total:

X = ∑ƒ x/∑ƒ

X = 21624.1/525

X =41.114

Calculation op Geometric Mean:

log G.M =∑ƒ (log X)/n

log G.M = 832.95/525.95

log G.M = 1.5837

G.M Anti log = 1.5837 = 38.34

Calculation of Harmonic Mean:

H.M = n/∑ (ƒ/x)

H.M = 525.95/14.859

H.M = 35.39

TABLE NO: 5 UN EMPLOYED RATES FOR MALE AND FEMALE:

C - I	F	C – B	X	FX	F	FX	log x	F(log x)	F(log x)	F/X	F/x
10 – 14	22	9.5 - 14.5	12	264	37	444	1.079	23.738	39.923	1.833	3.083
15 – 19	13	14.5 –19.5	17	221	21	357	1.230	15.99	25.83	0.764	1.235
20 – 24	7	19.5 –24.5	22	154	20	440	1.342	9.394	26.84	0.318	0.909
25 – 29	4	24.5 - 29.5	27	108	17	459	1.431	5.724	24.327	0.148	0.629
30 – 34	2	29.5 – 34.5	32	64	8	256	1.505	3.01	12.04	0.062	0.25
35 – 39	1	34.5 – 39.5	37	37	2	74	1.568	1.568	3.136	0.027	0.054
40 – 44	1	39.5 – 44.5	42	42	5	210	1.623	1.623	8.115	0.023	0.119
45 – 49	1	44.5 – 49.5	47	47	8	376	1.672	1.672	13.376	0.021	0.3170
50 – 54	3	49.5 – 54.5	52	156	22	1144	1.716	5.148	37.752	0.057	0.423
55 – 59	5	54.5 – 59.5	57	285	37	2109	1.755	8.775	64.935	0.087	0.649
60 – 64	12	59.5 – 64.5	62	744	62	3844	1.792	21.504	111.10	0.193	1
65 – 69	14	64.5 – 69.5	67	938	67	4489	1.826	25.564	122.34	0.208	1
SUM	85			3060	306	14202		122.71	612.06	3.741	9.521

Calculation of Arithmetic Mean:

For Male:

X = ∑ƒ X/∑ƒ

X = 3060/85 = 36.42

For Male:

X = 14202/306

X = 46.41

Calculation of Geometric Mean:

For Male:

Log G.M = ∑ƒ.log x/n

Log G.M = 122.71/85

Log G.M = 1.443

G.M Antilog = 1.443

G.M = 27.73

For Female:

Log G.M = 865.34/306

G.M Antilog = 1.827

G.M = 26.63

Calculation of Harmonic Mean:

For Male:

H.M = n/∑ (ƒ/x)

H.M = 85/3.741

H.M = 23

For Female:

H.M = 306/9.521

H.M = 32.13

CONTENTS

• INTRODUCTION
• MEASURE OF CENTRAL TENDENCY
• DIFFINITIONS OF:
• ARITHEMETIC MEAN
• GEOMETRIC MEAN
• HARMONIC MEAN
• FORMULAS FOR THESE MEASURES
• MATHIMATICAL CALCULATION
• FIGURES AND TABLES
• RELATIONSHIP / IMPHERICAL RELATIONSHIP
• PROPERTIES AND ANALIYSIS
• CONCLUSION
• REFRENCE

TITLE: MEASURE OF CENTRAL TENDENCY

Posted in: MBA Reports,Report Research