दिलेल्या संख्यांचा मध्य शोधा:

 वर्ग अंतराळ 10-20 20-30 30-40 40-50 50-60 60-70 70-80
वारंवारता 9 13 6 4 6 2 3

  1. 39.95
  2. 35.70
  3. 43.95
  4. 23.95

Answer (Detailed Solution Below)

Option 2 : 35.70
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Detailed Solution

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वापरलेले सूत्र:

गटबद्ध संख्यांचा मध्य याद्वारे दिला जातो,

\(\bar X\ = \frac{∑ f_iX_i}{∑ f_i}\)

जेथे, \(u_i \ = \ \frac{X_i\ -\ a}{h}\)

Xi = वर्ग i चा मध्य

f= i वर्गाशी संबंधित वारंवारता

दिलेल्याप्रमाणे:

 वर्ग अंतराळ 10-20 20-30 30-40 40-50 50-60 60-70 70-80
वारंवारता 9 13 6 4 6 2 3

 

गणना:

आता, संख्यांच्या सरासरीची गणना करण्यासाठी  ∑fiXi आणि ∑fi  खालीलप्रमाणे शोधावे लागतील,

 वर्ग अंतराळ fi Xi fiXi
10 - 20 9 15 135
20 - 30 13 25 325
30 - 40 6 35 210
40 - 50 4 45 180
50 - 60 6 55 330
60 - 70 2 65 130
70 - 80 3 75 225
  ∑fi = 43 ∑X = 350 ∑fiXi = 1535

तर,

आपणास माहित आहे, गटबद्ध संख्यांचा मध्य याद्वारे दिला जातो,

\(\bar X\ = \frac{∑ f_iX_i}{∑ f_i}\)

\(\frac{1535}{43}\)

= 35.7

म्हणून, गटबद्ध संख्यांचा मध्य 35.7 आहे.

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