Question

Which box-and-whisker plot satisfies the given information? lower extreme: 5 interquartile range: 10 median: 15 upper quartile: 22.5 range: 25

Answer 1

To create a box-and-whisker plot, order the data, calculate the five-number summary (minimum, Q1, median, Q3, maximum), draw a number line, and then draw a box with whiskers extending to the minimum and maximum values.

Step-by-step explanation:

To graph a box-and-whisker plot for the data values provided (10, 10, 10, 15, 35, 75, 90, 95, 100, 175, 420, 490, 515, 515, 790), follow these steps:

1. Begin by ordering the data from least to greatest if it's not already sorted.
2. Identify the minimum and maximum values of the data set. Here, the minimum value is 10 and the maximum value is 790.
3. Calculate the median (Q2), which is the middle number when the data is in order. If there's an even number of data points, average the two middle numbers. For the provided set, the median is 95.
4. Find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half. In this case, Q1 is 10 and Q3 is 515.
5. Compute the interquartile range (IQR) by subtracting Q1 from Q3. IQR = Q3 - Q1 = 515 - 10 = 505.
6. Draw a number line that includes the range of your data.
7. Mark the minimum, Q1, median, Q3, and the maximum on the number line and draw a box from Q1 to Q3 with a vertical line at the median.
8. Draw whiskers from the ends of the box to the minimum and maximum values.

A histogram, a box plot, and a chart all provide visual representation of data distribution. The box plot shows the central 50% of scores within the box itself, and the spread of these scores indicated by the whiskers.