Question

The mean height of a class of 28 students is 162 cm. A new student of height 149 cm joins the class. What is the mean height of the class now?

Answer 1

Answer on question #46853 - Math - Statistics and Probability

Question:

The mean height of a class of 28 students is $162~\mathrm{cm}$. A new student of height $149~\mathrm{cm}$ joins the class. What is the mean height of the class now?

Solution:

Denote $x_n$ the height of the $n$-th student. Then the mean height of the class at the beginning was

$$\frac{1}{28} \sum_{n=1}^{28} x_n = 162.$$

Then $\sum_{n=1}^{28} x_n = 162 * 28 = 4536$.

After the new student joins the class, the mean height will be

$$\frac{1}{29} \left( \sum_{n=1}^{29} x_n \right) = \frac{1}{29} \left( \sum_{n=1}^{28} x_n + x_{29} \right) = \frac{1}{29} (4536 + 149) = \frac{4685}{29} = 161 \frac{16}{29}.$$

Answer: $161 \frac{16}{29}$.

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