Question

Draw a box-and-whisker plot of the data. $$10,5,9,50,10,3,4,15,20,6$$

Short answer

The Box-and-Whisker plot for the given data can be drawn with Q1 at 5.5, median (Q2) at 9.5, Q3 at 17.5. The smallest data point is 3 and the largest is 50. After drawing, the plot reveals no outliers from this data.

Step-by-step solution

Arrange the data in increasing order

First, arrange the given numbers in increasing order. This helps in identifying the median and quartiles of the data. The sorted data becomes \[3, 4, 5, 6, 9, 10, 10, 15, 20, 50\]

Calculate the Quartiles

Next, find the first quartile (Q1), the median (Q2), and the third quartile (Q3). We have 10 data points so: \n- The Median (Q2) is the average of 5th and 6th numbers, i.e., 9.5. \n- Q1 value is a median of the first half numbers, so average of 5 and 6, i.e., 5.5. \n- Q3 is median of the second half numbers, so it is the average of 15 and 20, i.e., 17.5

Draw the Box-and-Whisker plot

Now, draw a number line and mark the quartile values and extreme data on it. Draw a box from Q1 to Q3 and draw lines (known as whiskers) from Q1 to the smallest data point and from Q3 to the largest data point. Place a line in the box at Q2 (the median).

Interpret the Box-and-Whisker plot

The 'Box' in the plot represents the middle 50% of the data, the 'whiskers' represent the data outside the middle 50%. Any data point that lies beyond the 'whiskers' is considered as an outlier.