The mean of 200 numbers is 180 If each number is increased by 10,then what is the value of the - Maths - Statistics

Question

The mean of 200 numbers is 180 If each number is increased by
10,then what is the value of the new mean?

Ajanta Trivedi · Accepted Answer

the mean of 200 numbers is 180 $\frac{\sum_{i = 1}^{200} x_{i}}{200} = 180 \sum_{i = 1}^{200} x_{i} = 180 * 200 = 36000 (1)$ if each number is increased by 10, new mean of 200 numbers is $M = \frac{\sum_{i = 1}^{200} (x_{i} + 10)}{200} = \frac{\sum_{i = 1}^{200} x_{i} + 10 \sum_{i = 1}^{200} 1}{200} = \frac{36000 + 10 * 200}{200} = \frac{36000 + 2000}{200} = \frac{38000}{200} = 190$ therefore the new mean is 190

The mean of 200 numbers is 180.If each number is increased by 10,then what is the value of the new mean?