Question

1. the dot plots show 9 scores on a 10 - question trivia game for two students. select all true statements about the dot plots. a. noahs scores have greater variability than jadas scores. b. the standard deviation of noahs scores is equal to the standard deviation of jadas scores. c. the mean of noahs scores is greater than the mean of jadas scores. d. noahs mean is equal to noahs median.

Explanation:

Step1: Analyze variability

Variability can be visually assessed by the spread of data points in dot - plots. Noah's scores are more spread out, so Noah's scores have greater variability than Jada's scores. So, statement a is true.

Step2: Compare standard deviations

Standard deviation measures the amount of variation or dispersion of a set of values. Since Noah's data is more spread out, the standard deviation of Noah's scores is greater than that of Jada's scores. So, statement b is false.

Step3: Calculate and compare mean and median for Noah

For Noah's scores: 1, 2, 3, 4, 5, 5, 6, 7. Mean $\bar{x}=\frac{1 + 2+3 + 4+5+5+6+7}{8}=\frac{33}{8}=4.125$. Median: Arrange in ascending order, there are 8 data points, so median is the average of 4th and 5th values, $\frac{4 + 5}{2}=4.5$. The mean of Noah's scores is less than the median. So, statement c is false.

Step4: Check mean - median equality for Noah

As calculated above, Noah's mean ($4.125$) is not equal to Noah's median ($4.5$). So, statement d is false.

Answer:

A. Noah's scores have greater variability than Jada's scores.