Given a frequency distribution with most data values clustered to the left and a long tail extending to the right, what is the shape of the distribution shown?

• A. Symmetrical
• B. Negatively skewed (left-skewed)
• C. Positively skewed (right-skewed)
• D. Uniform

Answer: (C)

Verified step by step guidance

1. Understand the terminology: A distribution's shape describes how data values are spread out. Common shapes include symmetrical, skewed (positively or negatively), and uniform.
2. Identify the meaning of 'clustered to the left with a long tail to the right': This means most data points are concentrated on the lower values (left side), and fewer data points stretch out towards higher values (right side).
3. Recall the definition of skewness: If the tail of the distribution extends to the right (higher values), it is called positively skewed or right-skewed. Conversely, if the tail extends to the left (lower values), it is negatively skewed or left-skewed.
4. Match the description to the correct skewness: Since the data clusters on the left and the tail extends to the right, the distribution is positively skewed (right-skewed).
5. Confirm that the other options do not fit: Symmetrical means the data is evenly spread on both sides, negatively skewed means the tail is on the left, and uniform means data is evenly distributed across values.