Question

question 13(multiple choice worth 2 points) (appropriate measures mc) the number of meters a student swam this week are listed. 250, 500, 500, 650, 700, 700 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 about 550. the median is the best measure of variability and equals 575. the range is the best measure of variability and equals 450. the iqr is the best measure of variability and equals 200.

Explanation:

Step1: Arrange data in ascending order

250, 500, 500, 650, 700, 700

Step2: Calculate mean

Mean = $\frac{250 + 500+500 + 650+700+700}{6}=\frac{3300}{6}=550$

Step3: Calculate median

Since there are 6 data - points, median is the average of the 3rd and 4th ordered values. Median=$\frac{500 + 650}{2}=575$

Step4: Calculate range

Range = Max - Min = 700 - 250 = 450

Step5: Calculate IQR

First, find the first quartile ($Q_1$) and third quartile ($Q_3$). The lower half of the data is 250, 500, 500, so $Q_1 = 500$. The upper half of the data is 650, 700, 700, so $Q_3=700$. IQR=$Q_3 - Q_1=700 - 500 = 200$
The range is a measure of variability. It is calculated as the difference between the maximum and minimum values in the data - set. Here, range = 450.

Answer:

B. The range is the best measure of variability and equals 450.