Plot a drapht with the above grouped data. Using the frequency and class midpoint. Explain skewness distribution

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. A distribution is skewed if it is not symmetrical on both sides of its central peak.

• Positive Skew (Right Skew): The tail of the distribution is longer on the right side. This means there are more extreme values on the higher end. In a positively skewed distribution, typically the mean is greater than the median, which is greater than the mode ($\text{Mean} > \text{Median} > \text{Mode}$).
• Negative Skew (Left Skew): The tail of the distribution is longer on the left side. This means there are more extreme values on the lower end. In a negatively skewed distribution, typically the mean is less than the median, which is less than the mode ($\text{Mean} < \text{Median} < \text{Mode}$).
• Symmetrical Distribution: The distribution is balanced on both sides of its central peak. For a perfectly symmetrical distribution, the mean, median, and mode are all equal ($\text{Mean} = \text{Median} = \text{Mode}$).

For the given data:
The frequencies are $1, 3, 4, 7, 5, 4, 2$. The mode is at 64.5 (frequency 7).
The distribution has a longer tail towards the higher values (right side) compared to the lower values.

• Mean $\approx 66.92$
• Median $\approx 66.64$
• Mode $= 64.5$ Since $\text{Mean} > \text{Median} > \text{Mode}$, the distribution is positively skewed (or right-skewed).