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.