A distribution with a mean of 200 units, a standard deviation of 40 units, a minimum value of 4 units and a maximum value of 245 units is
A. Positively skewed
B. Negatively skewed
C. "Bell-shaped"
D. Bi-modal
The value of 4 is much further from the mean than 245, especially in terms of standard deviations (1+ vs. almost -5 respectively). It would be negatively skewed (many scores at the high end, relatively few at the low end).
Thank You! I really appreciate you taking the time to answer my questions.
With the same mean and st.deviation, but a min of 55 and a max of 330, what would that be? I just need another example explained...thanks.
Figure how many standard deviations (SDs) above and below the mean each extreme is. If they are approximately equal, it is "bell-shaped." If one is significantly further away in terms of SDs, it is skewed in that direction. (You have to decide what is significant.)
There is insufficient data to suggest bimodal.
I hope this helps a little more.
To determine the shape of the distribution, we need to analyze the mean, standard deviation, and the range of the data.
A positively skewed distribution means that the tail of the distribution extends towards the right side, meaning there are more low values in the dataset. Conversely, a negatively skewed distribution means that the tail extends towards the left side, indicating more high values in the dataset.
A "bell-shaped" distribution, or a normal distribution, is symmetrical and has most of the data clustered around the mean, with a gradual decrease in frequency towards both tails.
To determine if the distribution is positively or negatively skewed, we compare the mean, median, and mode of the distribution. If the mean is greater than the median and the median is greater than the mode, the distribution is positively skewed. If the mean is less than the median and the median is less than the mode, the distribution is negatively skewed.
Given that the mean is 200 units, the minimum value is 4 units, and the maximum value is 245 units, we can see that the mean is closer to the maximum value. This implies that there are more high values in the dataset, suggesting a possible positive skewness.
However, we also need to consider the standard deviation. A large standard deviation indicates a wide spread of values and can affect the skewness. In this case, the standard deviation is 40 units, which is relatively large compared to the range of the data. This suggests that the data is more spread out, which could potentially affect the skewness.
Without calculating the exact values of the median and mode, it is difficult to determine the skewness for sure. However, based on the given information and the relative positions of the mean and the range of the data, it is most likely that the distribution is positively skewed (Option A).
To confirm the skewness or determine the exact skewness value, you would need to calculate the median and mode of the distribution and compare them to the mean, or construct a histogram or box plot of the data. These calculations can be performed using statistical software or by performing the calculations manually.