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intermediate20 min

Quantitative Reasoning: Data Analysis

Computing mean, median, and range from a described data set, and avoiding unsupported extrapolation.

What you'll learn

  • Extract specific values accurately from a described data table
  • Calculate mean, median, and range from a small original data set
  • Distinguish a conclusion the data actually supports from an unsupported extrapolation beyond it

Explanation

Data Analysis questions describe data using tables, bar or line graphs, or other summaries, and ask you to extract specific values or compute statistical measures: mean, median, mode, range, standard deviation (usually conceptually), percentiles, and basic probability. Since this practice lesson has no chart-rendering component, the data below is presented as a described table directly in text -- a format the real exam also uses for some Data Analysis questions.

Consider this original data set: a small bakery recorded the number of loaves of bread sold each day for one week: Monday 42, Tuesday 55, Wednesday 38, Thursday 61, Friday 47, Saturday 70, Sunday 35.

To find the mean, sum all seven values (42 + 55 + 38 + 61 + 47 + 70 + 35 = 348) and divide by 7, giving approximately 49.7. To find the median, sort the values first -- 35, 38, 42, 47, 55, 61, 70 -- and take the middle (fourth) value, which is 47; skipping the sort step is a common source of error. The range is the maximum minus the minimum: 70 - 35 = 35.

A separate but equally important skill is recognizing the limits of what a data set actually supports. If a question asks only about the seven days of data given, a conclusion like "sales will follow this exact same pattern next month" is an unsupported extrapolation -- the data describes one specific week, and nothing in it establishes a future trend. Distinguishing a computed fact about the given data from a speculative claim beyond it is exactly what many Data Analysis questions are testing.

Common mistakes

  • Computing the mean correctly but reporting the median (or vice versa) when the question specifically asked for the other one.
  • Forgetting to sort the values in order before identifying the median, leading to the wrong middle value.
  • Treating a conclusion about a future trend as supported by the data, when the question only asked about the specific data set actually given.

Knowledge check

Knowledge check

1. Using the bakery's weekly data (42, 55, 38, 61, 47, 70, 35 loaves sold Monday through Sunday), what is the mean number of loaves sold per day, rounded to one decimal place?
2. What is the median of the same weekly data set?
3. What is the range of the same weekly data set?
4. If a question asks only about the seven days of bakery data given, which of the following would be an unsupported conclusion?

Takeaway

Sort values before finding the median, keep mean/median/range clearly separate in your mind, and never treat a small data set as proof of a future trend it wasn't asked to establish.

Summary

Data Analysis rewards careful extraction and calculation (mean, median, range) from a given data set, plus recognizing when a conclusion goes beyond what the data actually supports.

References

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Next: Quantitative Reasoning: Quantitative Comparison Strategy →