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In statistics, the mean and median are two measures of central tendency. They both describe the center of a dataset, but they do so differently. The **mean** is the average of all the data points. You calculate it by summing all values and dividing by the number of values. The **median**, on the other hand, is the middle value when the data is ordered from smallest to largest. It splits the data into two equal halves.

• If the mean is higher than the median, it can indicate a right-skewed distribution, meaning a few larger values are pulling the average up.


• If the mean is lower than the median, it suggests a left-skewed distribution, where a few smaller values are bringing the average down.

In our exercise, the mean (141.7) is greater than the median (133.2). This suggests the distribution of weights is right-skewed, implying the presence of some heavier values affecting the average.

Quartiles are values that divide your dataset into four equal parts. They are composed of:

• **Q1 (First Quartile):** This is the middle value between the smallest data point and the median. It comprises the lowest 25% of the data.


• **Q3 (Third Quartile):** This is the middle value between the median and the highest data point, including the top 25% of the dataset.

The difference between Q3 and Q1 is known as the **Interquartile Range (IQR)**. It measures the spread of the middle 50% of the data.
In this exercise, Q1 is 118.3, Q3 is 157.3, making the IQR 39 (157.3 - 118.3). If the **median** is not centered in the IQR, it adds evidence to skewness. Here, the median (133.2) is closer to Q1 than Q3, which reinforces the idea that the distribution of weights is right-skewed.

Skewness is a measure of asymmetry in a distribution. When a distribution is perfectly symmetrical, it is said to have zero skewness.
- **Right Skew (Positive Skew):** If the distribution has a long tail on the right side. The mean is greater than the median. - **Left Skew (Negative Skew):** If the distribution has a long tail on the left side. The mean is less than the median.
In this exercise, the higher mean compared to the median indicates positive skewness or a right-skewed distribution for the weights. This is confirmed by the quartile analysis, where the median is not centered but leans towards the lower quartile. Skewness helps us understand the shape of our data, indicating whether there are outliers pulling the distribution in a particular direction.