Question

The given stem-and-leaf plot shows the distribution of the growth (in inches) of different plants in a nursery in a month. If the mean of the given data is 5.7, which of the following could be the values of A and B?

• A. 𝐴 = 0. 2, 𝐵 = 0. 6
• B. 𝐴 = 0, 𝐵 = 0. 9
• C. 𝐴 = 0. 3, 𝐵 = 0. 9
• D. 𝐴 = 0. 3, 𝐵 = 0. 5

Answer 1

The correct option is B 𝐴 = 0, 𝐵 = 0. 9

We can see that the values are 7.3, 7.4, 6.3, 6.5, 6.7, 5.2, 5.3, 5.4, 3.A, and 3.B.

$\text{Mean}=\frac{7.3+7.4+6.3+6.5+6.7+5.2+5.3+5.4+3.A+3.B}{10}$

$5.7=\frac{7.3+7.4+6.3+6.5+6.7+5.2+5.3+5.4+3.A+3.B}{10}$

$5.7=\frac{50.1+3.A+3.B}{10}$

$5.7\times 10=\frac{50.1+3.A+3.B}{10}\times 10$

50. 1 + 3. 𝐴 + 3. 𝐵 = 57
50. 1 + 3. 𝐴 + 3. 𝐵 − 50. 1 = 57 − 50. 1
3. 𝐴 + 3. 𝐵 = 57 − 50. 1
3. 𝐴 + 3. 𝐵 = 6. 9
Using place value method of addition, we get
𝐴 + 𝐵 = 0. 9.

Of the given options, this is possible only when 𝐴 = 0 and 𝐵 = 0.9.