Resourceaholic: Teaching Box and Whisker Plots - Free Printable
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Step-by-step solution for: Resourceaholic: Teaching Box and Whisker Plots
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Show Answer Key & Explanations
Step-by-step solution for: Resourceaholic: Teaching Box and Whisker Plots
To analyze the given boxplots and determine which statements are true, let's break down the information provided by the boxplots for both boys and girls. Here's a step-by-step explanation:
1. Minimum Value: The smallest value in the dataset.
2. First Quartile (Q1): The median of the lower half of the data.
3. Median (Q2): The middle value of the dataset.
4. Third Quartile (Q3): The median of the upper half of the data.
5. Maximum Value: The largest value in the dataset.
6. Interquartile Range (IQR): The range between Q3 and Q1, indicating the spread of the middle 50% of the data.
7. Skewness: Indicated by the symmetry or asymmetry of the boxplot. If the whiskers are longer on one side, the data is skewed in that direction.
#### Boys' Boxplot:
- Minimum: Approximately 140 cm
- Q1: Approximately 160 cm
- Median (Q2): Approximately 170 cm
- Q3: Approximately 175 cm
- Maximum: Approximately 185 cm
- Spread: The IQR (from Q1 to Q3) is relatively wide, indicating more variability in height among boys.
- Skewness: The right whisker is longer than the left whisker, suggesting a slight right skew.
#### Girls' Boxplot:
- Minimum: Approximately 145 cm
- Q1: Approximately 155 cm
- Median (Q2): Approximately 165 cm
- Q3: Approximately 170 cm
- Maximum: Approximately 180 cm
- Spread: The IQR (from Q1 to Q3) is narrower compared to boys, indicating less variability in height among girls.
- Skewness: The right whisker is slightly longer than the left whisker, suggesting a slight right skew.
1. The girls are taller on average.
- False. The median height for boys is approximately 170 cm, while the median height for girls is approximately 165 cm. Boys are taller on average.
2. The boys are taller on average.
- True. As explained above, the median height for boys (170 cm) is higher than the median height for girls (165 cm).
3. The girls show less spread in height.
- True. The IQR for girls (from Q1 to Q3) is narrower compared to the IQR for boys, indicating less variability in height among girls.
4. The boys show less spread in height.
- False. The IQR for boys is wider than the IQR for girls, indicating more variability in height among boys.
5. The shortest person is a girl.
- False. The minimum height for boys is approximately 140 cm, while the minimum height for girls is approximately 145 cm. The shortest person is a boy.
6. The tallest person is a boy.
- True. The maximum height for boys is approximately 185 cm, while the maximum height for girls is approximately 180 cm. The tallest person is a boy.
7. Both data sets are skewed to the left.
- False. Both boxplots show longer right whiskers, indicating a right skew, not a left skew.
8. Half the boys are over 172 cm tall.
- False. The median height for boys is approximately 170 cm, meaning half the boys are below 170 cm and half are above 170 cm. Therefore, not half the boys are over 172 cm.
9. Half the girls are under 165 cm tall.
- True. The median height for girls is approximately 165 cm, meaning half the girls are below 165 cm and half are above 165 cm.
The true statements are:
- 2. The boys are taller on average.
- 3. The girls show less spread in height.
- 6. The tallest person is a boy.
- 9. Half the girls are under 165 cm tall.
$$
\boxed{2, 3, 6, 9}
$$
Key Components of a Boxplot:
1. Minimum Value: The smallest value in the dataset.
2. First Quartile (Q1): The median of the lower half of the data.
3. Median (Q2): The middle value of the dataset.
4. Third Quartile (Q3): The median of the upper half of the data.
5. Maximum Value: The largest value in the dataset.
6. Interquartile Range (IQR): The range between Q3 and Q1, indicating the spread of the middle 50% of the data.
7. Skewness: Indicated by the symmetry or asymmetry of the boxplot. If the whiskers are longer on one side, the data is skewed in that direction.
Analysis of the Boxplots:
#### Boys' Boxplot:
- Minimum: Approximately 140 cm
- Q1: Approximately 160 cm
- Median (Q2): Approximately 170 cm
- Q3: Approximately 175 cm
- Maximum: Approximately 185 cm
- Spread: The IQR (from Q1 to Q3) is relatively wide, indicating more variability in height among boys.
- Skewness: The right whisker is longer than the left whisker, suggesting a slight right skew.
#### Girls' Boxplot:
- Minimum: Approximately 145 cm
- Q1: Approximately 155 cm
- Median (Q2): Approximately 165 cm
- Q3: Approximately 170 cm
- Maximum: Approximately 180 cm
- Spread: The IQR (from Q1 to Q3) is narrower compared to boys, indicating less variability in height among girls.
- Skewness: The right whisker is slightly longer than the left whisker, suggesting a slight right skew.
Evaluating Each Statement:
1. The girls are taller on average.
- False. The median height for boys is approximately 170 cm, while the median height for girls is approximately 165 cm. Boys are taller on average.
2. The boys are taller on average.
- True. As explained above, the median height for boys (170 cm) is higher than the median height for girls (165 cm).
3. The girls show less spread in height.
- True. The IQR for girls (from Q1 to Q3) is narrower compared to the IQR for boys, indicating less variability in height among girls.
4. The boys show less spread in height.
- False. The IQR for boys is wider than the IQR for girls, indicating more variability in height among boys.
5. The shortest person is a girl.
- False. The minimum height for boys is approximately 140 cm, while the minimum height for girls is approximately 145 cm. The shortest person is a boy.
6. The tallest person is a boy.
- True. The maximum height for boys is approximately 185 cm, while the maximum height for girls is approximately 180 cm. The tallest person is a boy.
7. Both data sets are skewed to the left.
- False. Both boxplots show longer right whiskers, indicating a right skew, not a left skew.
8. Half the boys are over 172 cm tall.
- False. The median height for boys is approximately 170 cm, meaning half the boys are below 170 cm and half are above 170 cm. Therefore, not half the boys are over 172 cm.
9. Half the girls are under 165 cm tall.
- True. The median height for girls is approximately 165 cm, meaning half the girls are below 165 cm and half are above 165 cm.
Final Answer:
The true statements are:
- 2. The boys are taller on average.
- 3. The girls show less spread in height.
- 6. The tallest person is a boy.
- 9. Half the girls are under 165 cm tall.
$$
\boxed{2, 3, 6, 9}
$$
Parent Tip: Review the logic above to help your child master the concept of comparing box and whisker plots worksheet.
