how do I determine whether or not a histogram is symmetrical, skewed right, skewed left, or cannot be determined
To determine whether a histogram is symmetrical, skewed right, skewed left, or cannot be determined, you need to examine the shape of the distribution. Here are the steps to follow:
1. Look at the overall shape of the histogram: Examine the distribution of the data displayed by the histogram. Is it generally bell-shaped, with the left and right sides being roughly symmetrical? Or does it have a longer tail on one side or the other?
2. Identify the mode: Determine the most frequently occurring value (mode) in the data. Is it closer to the left side or the right side of the histogram?
3. Check for symmetry: If the histogram is basically bell-shaped, with data evenly distributed on both sides of the mode, it is symmetrical. In a symmetrical histogram, the mean, median, and mode all coincide.
4. Observe skewness: If the histogram has a longer tail on the right side and the mode is closer to the left side, it is skewed right (positively skewed). This indicates that the majority of the data is concentrated towards the lower values. On the other hand, if the histogram has a longer tail on the left side and the mode is closer to the right side, it is skewed left (negatively skewed). This indicates that the majority of the data is concentrated towards the higher values.
5. Consider the presence of outliers: Outliers, which are extreme values that deviate significantly from the rest of the data, may affect the shape of the histogram. If there are outliers present, the shape and skewness may be distorted.
6. Determine if it cannot be determined: In some cases, the shape of the histogram may not be clear due to various factors, such as a small sample size or data that does not follow a specific pattern. In these cases, it may not be possible to definitively identify the type of skewness.
Always remember to consider multiple factors and interpret the histogram in the context of the data set and the intended analysis.