For each of the following sets of data, sketch the box plot and state whether it shows positive skew, negative skew or no skew.
a) 3, 4, 5, 5, 6, 7, 13, 14, 14, 16, 18
b) 4, 6, 7, 7, 9, 10, 11, 13, 13, 14, 16
c) 1, 2, 5, 5, 9, 12, 13, 15, 15, 16, 18
For each of the following sets of data, sketch the box plot and state whether it shows positive skew, negative skew or no skew
Share
Let’s analyze the data sets one by one to create box plots and determine skewness:
### a) Data: 3, 4, 5, 5, 6, 7, 13, 14, 14, 16, 18
1. Order the data: Already in order.
2. Find the median: The median is the middle value, which is 7.
3. Find Q1 and Q3:
– Q1 (lower quartile) = median of the first half = 5
– Q3 (upper quartile) = median of the second half = 14
4. Minimum and Maximum:
– Minimum = 3, Maximum = 18.
5. Box Plot: Draw a box from Q1 (5) to Q3 (14), with a line at the median (7).
– Whiskers extend from 3 to 5 (left) and from 14 to 18 (right).
Skewness: This plot is positively skewed since the tail on the right side (higher values) is longer.
### b) Data: 4, 6, 7, 7, 9, 10, 11, 13, 13, 14, 16
1. Order the data: Already in order.
2. Find the median: The median