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Justifying Data Features

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Justifying Data Features

Use the supplied data displays and context to describe and justify statistical features. Support claims with values from the displays. An unusual value is not automatically an error: consider plausible explanations and acknowledge what the data cannot establish.

A. Rainfall and unusual values

A volunteer records rainfall at one site in a New Zealand town. The monthly totals (mm) are: 61, 74, 78, 82, 84, 85, 86, 91, 96, 103, 111, 180. Using the median-of-halves method, Q1 = 80, median = 85, and Q3 = 99.5. The unusually high March total of 180 mm followed a period of heavy rain.

1.Calculate the interquartile range (IQR) and the upper outlier fence, using Q3 + 1.5 × IQR. Is 180 mm an outlier by this rule? Show your calculations.

2.Give a plausible contextual explanation for the high rainfall value, and state why the data alone cannot prove that explanation.

3.The rainfall values are mostly between 61 mm and 111 mm, with one value at 180 mm. Describe the distribution's shape and explain how the unusual high value could affect the mean compared with the median.

B. Study time and assessment results

A teacher compares study time and assessment score for 10 students. Each point is one student; study time is in hours and score is a percentage. No student names are included.

Study time (h)

Assessment score (%)

(1, 48)

(2, 55)

(2, 61)

(3, 63)

(3, 70)

(4, 72)

(4, 78)

(5, 82)

(6, 88)

(8, 45)

4.Plot the data pairs on axes labelled study time (hours) and assessment score (%). Describe the overall association, referring to the plotted points.

5.The point (8, 45) does not fit the main pattern well. Explain why it may be called an outlier in this relationship, and give one plausible explanation that does not assume the student did not study.

6.A classmate says, “This graph proves that studying longer causes higher scores.” Evaluate this claim using the data and statistical language.

C. Choosing a fair summary

A local online listing reports residential sale prices in a Wellington suburb. Most sales are in the middle price range, but a small number of unusually expensive homes extend the distribution towards higher prices.

7.For the sale-price data, the mean is $850,000 and the median is $720,000. Explain why these statistics differ and recommend which is more useful for describing a typical sale price. Justify your choice.

8.A report gives the median house price but leaves out the IQR. Explain what extra information the IQR would provide and why it could matter to someone comparing two suburbs.

9.An online article shows monthly traffic crashes as bars for each month, while another version joins the same monthly counts with a line. The goal is to compare the number of crashes in each month and notice seasonal differences. Which display is more appropriate, and what could make either display misleading?