Question

the dot plots represent the distributions of values in data sets a and b. data set a data set b dot - plot images not included in ocr. which of the following statements must be true? i. the median of data set a is equal to the median of data set b. ii. the standard deviation of data set a is equal to the standard deviation of data set b. a i only b ii only c i and ii d neither i nor ii

Explanation:

Step1: Find the number of data - points in each set

Count the dots in Data Set A and Data Set B. Both have 1 + 5+ 3 + 4+ 1+ 2=16 data - points.

Step2: Calculate the median position

For a set with \(n = 16\) data - points, the median is the average of the \(\frac{n}{2}=8\)th and \((\frac{n}{2}+1) = 9\)th ordered data - points.

Step3: Determine the median for Data Set A

Arrange the data in ascending order. Counting the dots, the 8th and 9th ordered data - points are both 12. So the median of Data Set A is \(\frac{12 + 12}{2}=12\).

Step4: Determine the median for Data Set B

Arrange the data in ascending order. Counting the dots, the 8th and 9th ordered data - points are both 12. So the median of Data Set B is \(\frac{12+12}{2}=12\).

Step5: Analyze the standard deviation

The standard deviation measures the spread of the data. Data Set A has a more concentrated distribution around the middle values compared to Data Set B which has some values more spread out (e.g., the single dot at 10 and 16 in Data Set B compared to Data Set A). So the standard deviation of Data Set A is not equal to the standard deviation of Data Set B.

Answer:

A. I only