Question

Which statement about the shape of the histogram is true?

1) The histogram is positively skewed
2) The histogram is negatively skewed
3) The histogram is symmetric
4) The shape of the histogram cannot be determined from the given information

Answer 1

Without the actual figure of the histogram or specific details regarding its shape, we cannot definitively state if it is positively skewed, negatively skewed, or symmetric. We need to analyze elements like the mean, median, and mode alignment or the presence of tails to determine the histogram's shape.

The correc6t answer is none of all.

Step-by-step explanation:

To determine the shape of a histogram, we should look for symmetry, skewness, and the presence of any modes. A histogram that is positively skewed means that there are more low values, and the tail of the distribution extends to the right. Conversely, a negatively skewed histogram indicates more high values, with a tail that extends to the left. A symmetric histogram would have mirror-image halves and typically has the mean and median at the same point. If the histogram is unimodal (having one mode), and that mode coincides with the mean and median, it further reinforces the symmetry of the distribution.

Without the actual histogram or additional information about the shape of the distribution, it is impossible to determine with certainty if the histogram is positively skewed, negatively skewed, or symmetric. However, based on the provided details, if the mean, median, and mode are the same, this would indicate a symmetric distribution. On the other hand, if there is a noticeable tail in one direction, it would suggest skewness in that direction.

Answer 2

The statement about the shape of the histogram that is true is 3) The histogram is symmetric. A histogram is symmetric when a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other.

Step-by-step explanation:

A histogram is symmetric when a vertical line can be drawn at some point in the histogram such that the shape to the left and the right of the vertical line are mirror images of each other. In a perfectly symmetrical distribution, the mean and the median are the same. In this case, the mean, median, and mode are all the same, which indicates a symmetrical distribution.

For example, if we have a set of data that follows a normal distribution, the histogram of the data will be symmetric. The bell-shaped curve of a normal distribution is a classic example of symmetry.

The information provided in the question does not indicate any skewness in the histogram, so options 1) The histogram is positively skewed and 2) The histogram is negatively skewed are not applicable. And since the mean, median, and mode are all the same, the histogram cannot be classified as having two modes, so option 4) The shape of the histogram cannot be determined from the given information is also not applicable. Therefore, the correct answer is 3) The histogram is symmetric.