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Mathematics

If the mean of the data y1, y2, y3, …., yn is 102, then the mean of the data 5y1, 5y2, 5y3, …., 5yn is :

  1. 102

  2. 204

  3. 510

  4. 606

Statistics

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Answer

Mean of y1, y2, y3, …., yn is 102

So,

y1+y2++ynn=102\dfrac{y1 + y2 + \dots + y_n}{n} = 102

New observation is :

5y1, 5y2, 5y3, …., 5yn

New Mean=5y1+5y2++5ynn=5(y1+y2++yn)n=5×(y1+y2++ynn)\text{New Mean} = \dfrac{5y1 + 5y2 + \dots + 5yn}{n} \\[1em] = \dfrac{5(y1 + y2 + \dots + yn)}{n} \\[1em] = 5 \times \left( \dfrac{y1 + y2 + \dots + y_n}{n} \right)

Since,

y1+y2++ynn=102\dfrac{y1 + y2 + \dots + y_n}{n} = 102

New Mean=5×102\text{New Mean} = 5 \times 102 = 510.

Hence, option 3 is the correct option.

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