Question

the dot - plot shows 9 scores on a 10 - question quiz for two students. select all the statements that must be true. a. destinys scores have greater variability than yuniers scores. b. the mean of destinys scores is greater than the mean of yuniers scores. c. using only destinys scores, the mean is equal to the median. d. destiny scored better than yunier on every assignment. e. the standard deviation of destinys scores is equal to the standard deviation of yuniers scores.

Explanation:

Step1: Analyze variability

Destiny's scores are more spread - out than Yunier's. Range of Destiny's scores is larger, so variability is greater.

Step2: Calculate means (assume scores are discrete points)

Let's assume the scores for Destiny are \(x_1,x_2,\cdots,x_n\) and for Yunier are \(y_1,y_2,\cdots,y_m\). Mean of Destiny's scores \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\), mean of Yunier's scores \(\bar{y}=\frac{\sum_{j = 1}^{m}y_j}{m}\). By visual inspection, we can't be sure which mean is greater.

Step3: Find median and mean for Destiny

Arrange Destiny's scores in ascending order. Since \(n = 9\) (odd number of data - points), median is the 5th value. Calculate the mean \(\bar{x}=\frac{\sum_{i=1}^{9}x_i}{9}\). By visual inspection, they are not equal.

Step4: Compare individual scores

We can see that there are some scores where Yunier scored higher than Destiny.

Step5: Analyze standard deviation

Since variability of Destiny's scores is greater, standard deviation of Destiny's scores is greater than Yunier's.

Answer:

A. Destiny’s scores have greater variability than Yunier’s scores.