Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
To determine the shape of the height and weight distributions, we need to calculate the mean and median for both distributions and compare them.
### Heights:
- Data: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
- Mean (Average): The mean of the height distribution is calculated by adding all the heights together and dividing by the number of data points.
[tex]\[ \text{Mean of heights} = \frac{178 + 163 + 174 + 186 + 154 + 167 + 167 + 181 + 159 + 165 + 177 + 191 + 158}{13} \approx 170.77 \][/tex]
- Median: The median is the middle value when the data is arranged in ascending order. For the height distribution:
Arranged data: 154, 158, 159, 163, 165, 167, 167, 174, 177, 178, 181, 186, 191
[tex]\[ \text{Median of heights} = 167.0 \][/tex]
#### Comparing Mean and Median for Heights:
- If the mean is greater than the median, the distribution is positively skewed.
- If the mean is less than the median, the distribution is negatively skewed.
- If the mean is equal to the median, the distribution is symmetric.
Since [tex]\( 170.77 > 167.0 \)[/tex], the height distribution is positively skewed.
### Weights:
- Data: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
- Mean (Average): The mean of the weight distribution is calculated similarly by adding all the weights and dividing by the number of data points.
[tex]\[ \text{Mean of weights} = \frac{157 + 163 + 190 + 187 + 183 + 173 + 184 + 189 + 193 + 192 + 177 + 173 + 168}{13} \approx 179.15 \][/tex]
- Median: The median is the middle value when the data is arranged in ascending order. For the weight distribution:
Arranged data: 157, 163, 168, 173, 173, 177, 183, 184, 187, 189, 190, 192, 193
[tex]\[ \text{Median of weights} = 183.0 \][/tex]
#### Comparing Mean and Median for Weights:
- If the mean is greater than the median, the distribution is positively skewed.
- If the mean is less than the median, the distribution is negatively skewed.
- If the mean is equal to the median, the distribution is symmetric.
Since [tex]\( 179.15 < 183.0 \)[/tex], the weight distribution is negatively skewed.
### Conclusion:
- The height distribution is positively skewed.
- The weight distribution is negatively skewed.
Therefore, the correct answer is:
[tex]\[ \boxed{E. \text{The height and weight distribution exhibit a positive and a negative skew, respectively.}} \][/tex]
### Heights:
- Data: 178, 163, 174, 186, 154, 167, 167, 181, 159, 165, 177, 191, 158
- Mean (Average): The mean of the height distribution is calculated by adding all the heights together and dividing by the number of data points.
[tex]\[ \text{Mean of heights} = \frac{178 + 163 + 174 + 186 + 154 + 167 + 167 + 181 + 159 + 165 + 177 + 191 + 158}{13} \approx 170.77 \][/tex]
- Median: The median is the middle value when the data is arranged in ascending order. For the height distribution:
Arranged data: 154, 158, 159, 163, 165, 167, 167, 174, 177, 178, 181, 186, 191
[tex]\[ \text{Median of heights} = 167.0 \][/tex]
#### Comparing Mean and Median for Heights:
- If the mean is greater than the median, the distribution is positively skewed.
- If the mean is less than the median, the distribution is negatively skewed.
- If the mean is equal to the median, the distribution is symmetric.
Since [tex]\( 170.77 > 167.0 \)[/tex], the height distribution is positively skewed.
### Weights:
- Data: 157, 163, 190, 187, 183, 173, 184, 189, 193, 192, 177, 173, 168
- Mean (Average): The mean of the weight distribution is calculated similarly by adding all the weights and dividing by the number of data points.
[tex]\[ \text{Mean of weights} = \frac{157 + 163 + 190 + 187 + 183 + 173 + 184 + 189 + 193 + 192 + 177 + 173 + 168}{13} \approx 179.15 \][/tex]
- Median: The median is the middle value when the data is arranged in ascending order. For the weight distribution:
Arranged data: 157, 163, 168, 173, 173, 177, 183, 184, 187, 189, 190, 192, 193
[tex]\[ \text{Median of weights} = 183.0 \][/tex]
#### Comparing Mean and Median for Weights:
- If the mean is greater than the median, the distribution is positively skewed.
- If the mean is less than the median, the distribution is negatively skewed.
- If the mean is equal to the median, the distribution is symmetric.
Since [tex]\( 179.15 < 183.0 \)[/tex], the weight distribution is negatively skewed.
### Conclusion:
- The height distribution is positively skewed.
- The weight distribution is negatively skewed.
Therefore, the correct answer is:
[tex]\[ \boxed{E. \text{The height and weight distribution exhibit a positive and a negative skew, respectively.}} \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.