Mathematics 9709 · AS & A Level · Sampling and estimation
Sampling and estimation — practice question
Barry has 20 oranges and 25 lemons. The oranges have a mean weight of $220\text{ g}$ and a standard deviation of $32\text{ g}$. The lemons have a mean weight of $118\text{ g}$ and a standard deviation of $12\text{ g}$.
(i)[2]
Calculate the mean weight of the $45$ fruits.
(ii)[5]
Let the individual weights of the oranges in grams be denoted by $x_o$, and let the individual weights of the lemons in grams be denoted by $x_l$. After finding $\sum x_o^2$ and $\sum x_l^2$, determine the variance of the weights of the $45$ fruits.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct use of the mean calculation $(220\times20+118\times25)/45$” …