First slide

Introduction to statistics

Question

If the mean of the distribution is 2.6, then the value of y is

Moderate

A

24
B

13
C

8
D

3

Solution

$\begin{array}{l} Mean = \frac{\sum_{i = 1}^{n} f_{i} x_{i}}{\sum_{i = 1}^{n} f_{i}} \\ ∴ 2.6 = \frac{1 \times 4 + 2 \times 5 + 3 \times y + 4 \times 1 + 5 \times 2}{4 + 5 + y + 1 + 2} \\ \Rightarrow 31.2 + 2.6 y = 28 + 3 y \Rightarrow 0.4 y = 3.2 \Rightarrow y = 8 \end{array}$

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