For the data X: 5,4,3,2,1; F: 5,3,1,3,5; what is the distribution shape?

For the data X: 5,4,3,2,1; F: 5,3,1,3,5; what is the distribution shape?

• A. Symmetrical
• B. Positively skewed
• C. Negatively skewed
• D. Normal

Answer: (A)

The data show symmetry around the center value. The frequencies mirror on either side: 5 at the ends (x = 1 and x = 5), 3 next (x = 2 and x = 4), and the center value (x = 3) has the smallest frequency. This mirrored pattern means the tails balance each other, which is the hallmark of a symmetrical distribution. A quick check enhances this: the mean is 3 (sum xF divided by total frequency) and the median is also 3, reinforcing that the center is balanced. It’s not a normal (bell-shaped) distribution because the center is the least frequent point and the ends peak, so it’s symmetric but not unimodal like a normal curve.

The data show symmetry around the center value. The frequencies mirror on either side: 5 at the ends (x = 1 and x = 5), 3 next (x = 2 and x = 4), and the center value (x = 3) has the smallest frequency. This mirrored pattern means the tails balance each other, which is the hallmark of a symmetrical distribution.

A quick check enhances this: the mean is 3 (sum xF divided by total frequency) and the median is also 3, reinforcing that the center is balanced. It’s not a normal (bell-shaped) distribution because the center is the least frequent point and the ends peak, so it’s symmetric but not unimodal like a normal curve.