Misrepresenting data and mean median mode guide

Both questions reward mechanism over opinion, and both are commonly answered with a general complaint about statistics being misleading. For the first, name the specific distortion and say what it does to the reader's perception. Truncating a vertical axis so it does not start at zero exaggerates small differences; stretching or compressing one axis changes an apparent slope without changing a single number; using area or volume to represent a one-dimensional quantity makes a doubling look like a quadrupling; selecting a start date so a trend begins at a local minimum manufactures growth; and omitting sample size or confidence intervals hides how little the difference is supported. Each of those is a technique with a name and an effect, and naming both is what separates an analytical answer from an impression that the news exaggerates. Three techniques described properly will carry this half of the post further than a longer list left unexplained.

The request for where you have seen it done is a real requirement, so give one instance you can describe concretely: a news chart, an advertisement claiming most dentists recommend, an election poll reported without a margin of error, a hospital quality scorecard, a graph in an article you read for another course. Describe what the display did and what a corrected version would show. It is worth being clear that misrepresentation does not require dishonesty. A truncated axis is standard in some fields and defensible when the variation is genuinely small, and a mean reported for a skewed distribution is often carelessness rather than deception, so the useful question is what the display makes a reader believe rather than what its author intended. Framing it that way also keeps the post analytical rather than accusatory, which matters when your example comes from a source your classmates may rely on.

The second question is really about distribution shape and level of measurement, and answering it in those terms is what earns the marks. The mean uses every value and is the right summary for roughly symmetric interval or ratio data, which is exactly why it is pulled by outliers and by skew: report a mean income or a mean length of stay and a small number of extreme cases will drag it away from anything typical. The median is positional, so it survives skew and outliers and works for ordinal data, at the cost of ignoring how far the extremes lie. The mode is the only option for nominal categories such as blood type or admitting diagnosis, and it is unstable in small samples and useless when values are nearly unique. Say which population characteristics decide this — skew, outliers, measurement level, sample size, multimodality — and give a clinical or everyday example of each.