Problems — 8.9 Statistics Foundations

1

**Reaction-distance dataset (department Numberphile, May 2026).** A class of 20 Year 8 students measured their reaction distance (cm): 15, 11, 19, 14, 12, 17, 21, 14, 17, 11, 23, 15, 20, 17, 13, 10, 20, 16, 12, 28. (a) Find the mean. (b) Find the median. (c) Find the mode. (d) Find the range. (e) Identify any value that may be an outlier and justify.

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2

**Effect of outlier on mean vs median.** Continuing the reaction-distance dataset: remove the largest value (28) and recompute the mean and median. (a) Find the new mean. (b) Find the new median. (c) Compare the shifts. Which measure is more robust?

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3

**Mean with an unknown value.** A class of 24 students has a mean test mark of 62. A new student joins and the class mean is now 63. (a) Find the new student's mark. (b) The teacher discovers one mark was misread: 78 should have been 87. Find the corrected mean.

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4

**Comparing two classes (means + ranges).** Class A reaction distances had mean 15 cm and range 18 cm. Class B had mean 17 cm and range 10 cm. (a) Which class had a faster (lower) average reaction? (b) Which class was more consistent (smaller range)? (c) Write a one-sentence comparison.

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5

**Frequency-table mean.** A frequency table records the number of pets per student in a class: | Pets | 0 | 1 | 2 | 3 | 4 | |------|---|---|---|---|---| | Frequency | 5 | 8 | 4 | 2 | 1 | (a) Find the total number of students. (b) Find the mean number of pets per student. (c) Find the median and modal number of pets.

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6

**Compute and compare measures.** Five students' weekly hours of homework: 8, 12, 6, 14, 10. (a) Find mean, median, mode, range. (b) An additional value 30 is added. Find the new mean, median and range. (c) Which measure changes the most?

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7

**Find a missing value with given mean.** A set of 5 numbers is 4, 9, $x$, 12, 16. The mean is 10. (a) Find $x$. (b) The number 16 is removed. Find the new mean.

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8

**Median with even count.** A set of 8 numbers, sorted, is: 5, 7, 9, 11, 12, 13, 16, 20. (a) Find the mean. (b) Find the median. (c) Find the range. (d) Identify any outlier and justify.

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9

**Combining two classes.** Class A has 12 students with mean 14. Class B has 18 students with mean 16. (a) Find the combined sum. (b) Find the combined mean. (c) Is the combined median equal to the average of the two class medians? Explain.

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10

**Mean and median together.** Five integers have sum 60 and median 12. (a) Suggest one set of values. (b) Find a set where the mean equals the median. (c) Find a set where the mean is much larger than the median, and identify why.

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11

**Modelling with tallies.** A teacher tallies the number of pets per student over 30 students: 0: //// //// / 1: //// //// 2: //// 3: / (a) Construct a frequency table. (b) Find the mean, median, and mode. (c) State the percentage of students with at least 2 pets.

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12

**Cleaning data.** A pupil records the heights (cm) of 10 students: 150, 152, 148, 155, 1500, 153, 149, 151, 154, 150. One value is clearly a typo. (a) Identify the typo. (b) Compute the (a) mean with the typo and (b) without. (c) Compute the median in both cases. (d) Which measure was the typo more disruptive to?

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