Question

question 7(multiple choice worth 2 points) (appropriate measures mc) the length of ribbons found at a seamstress are listed. 2, 10, 10, 12, 12, 20 what is the appropriate measure of variability for the data shown, and what is its value? the mean is the best measure of variability and equals 11. the median is the best measure of variability and equals 11.5. the range is the best measure of variability and equals 18. the iqr is the best measure of variability and equals 2. question 8(multiple choice worth 2 points) (proportions mc) the length - to - width ratio of a television screen is 4 to 3. mya bought a television with a length of 48 inches. what is the width of the television? 12 inches 24 inches 36 inches 42 inches

Explanation:

Question 7

Step1: Recall measure of variability

Mean and median are measures of central - tendency, not variability. Range and IQR are measures of variability.

Step2: Calculate the range

The range is calculated as the difference between the maximum and minimum values. The maximum value in the data set \(2,10,10,12,12,20\) is \(20\) and the minimum is \(2\). Range \(=20 - 2=18\).

Step3: Calculate the IQR

First, order the data: \(2,10,10,12,12,20\). The median of the lower half (\(Q1\)) for \(n = 6\) (the lower half is \(2,10,10\)) is \(10\). The median of the upper half (\(Q3\)) (the upper half is \(12,12,20\)) is \(12\). IQR \(=Q3 - Q1=12 - 10 = 2\). Since the data has no outliers (no extreme values that would skew the data significantly), the range is a good measure of variability.

Step1: Set up the proportion

Let the width of the television be \(x\) inches. The length - to - width ratio is \(\frac{4}{3}\), and the length is \(48\) inches. So we set up the proportion \(\frac{4}{3}=\frac{48}{x}\).

Step2: Cross - multiply

Cross - multiplying gives us \(4x=3\times48\).

Step3: Solve for \(x\)

First, calculate \(3\times48 = 144\). Then, \(x=\frac{144}{4}=36\).

Answer:

The range is the best measure of variability and equals 18.

Question 8