Question

question 29
a sample of n = 20 scores has a mean of m = 30. a second sample of n = 10 scores has a mean of m = 50. if the two samples are combined, the weighted sample mean will be less than 40.
2 pts
true
false
question 30
a distribution of scores has a mean of 52, a median of 54, and a mode of 56. based on this information, it appears that the distribution is symmetrical.
2 pts
true
false

Explanation:

Question 29

Step1: Recall weighted - mean formula

The formula for the weighted mean $\bar{X}=\frac{n_1M_1 + n_2M_2}{n_1 + n_2}$, where $n_1$ and $n_2$ are the sample sizes and $M_1$ and $M_2$ are the sample means.
Here, $n_1 = 20$, $M_1=30$, $n_2 = 10$, $M_2 = 50$.

Step2: Calculate the weighted mean

$\bar{X}=\frac{20\times30+10\times50}{20 + 10}=\frac{600 + 500}{30}=\frac{1100}{30}\approx36.67$.
Since $36.67<40$, the statement is True.

In a symmetrical distribution, the mean, median, and mode are equal. Here, the mean is 52, the median is 54, and the mode is 56. Since they are not equal, the distribution is not symmetrical.

Answer:

True

Question 30