NAME: ___________________________________________________________ DATE: _____________________
AP STATISTICS CH 1.3 DAY 2 – BOXPLOTS ACTIVITY
How to make a boxplot
1. A central box is drawn from the first quartile ( Q1 ) to the third quartile ( Q3 )
2. A line in the box marks the median
3. Lines (called whiskers) extend from the box to the smallest and largest observation that are not
outliers
Example: Who Has More Contacts—Males or Females?
The following data show the number of contacts that a sample of high school students had in their cell phones.
Male: 124 41 29 27 44 87 85 260 290 31 168 169 167 214 135 114 105 103 96 144
Female: 30 83 116 22 173 155 134 180 124 33 213 218 183 110
STATE:
PLAN:
DO:
NUMERICAL SUMMARY
n
x
sx
min
Q1
M
Q3
max
Male
Female
BOXPLOT
SHAPE:
CENTER:
SPREAD:
OUTLIERS:
CONCLUDE:
SOLUTION CH 1.3 DAY 2 BOXPLOTS & STANDARD DEVIATION
State: Do the data give convincing evidence that one gender has more contacts than the other?
Plan: We will compute numerical summaries, graph parallel boxplots, and compare shape, center, spread and unusual
values.
Do: Here are the numerical summaries and boxplots for each distribution:
n
Male
x
sx
min
20 121.65 74.45
27
Female 14 126.71 65.75
22
Q1
M
Q3
64.5 109.5 167.5
83
129
180
max
290
218
Male: 27, 29, 31, 41, 44, 85, 87, 96, 103, 105, 114, 124, 135, 144, 167, 168, 169, 214, 260, 290
Female: 22, 30, 33, 83, 110, 116, 124, 134, 155, 173, 180, 183, 213, 218
Shape: The female distribution is approximately symmetric but the male distribution is slightly skewed to the right.
Center: The median number of contacts for the females is slightly higher than the median number of contacts for the
males.
Spread: The distribution of contacts for males is more spread out than the distribution of females since both the IQR and
range is larger.
Outliers: Neither of the distributions have any outliers.
Conclude: Since the female distribution is roughly symmetric, we would use the mean (126.71 contacts); but, the male
distribution is skewed to the right so we will use the median (109.5 contacts) as the measure of center. The females
have more contacts than males. However, the differences are small so this is not convincing evidence that one gender
has more contacts than the other.