Revision and practice with answers
On this page 4 headings
Use this page after the lessons. Attempt each question before opening its answer.
Quick revision
| Idea | Remember |
|---|---|
| Population / sample | Whole group / subgroup studied |
| Descriptive / inferential | Describe observed data / extend beyond it |
| Case / variable / value | Row unit / characteristic / cell entry |
| Categorical / numerical | Labels / amounts |
| Cross-sectional / time series | Snapshot / chronological sequence |
| Nominal / ordinal / interval / ratio | Names / order / equal gaps / meaningful zero |
Practice with explained answers
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1. A survey asks 40 of a college’s 800 students about commute time. Identify population, sample, case and variable.
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Population: the 800 students. Sample: the 40 asked. Case: one student. Variable: commute time, with a unit such as minutes.
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2. The mean commute time of those 40 is reported. Then it is used to estimate the college mean. Classify each step.
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Reporting the 40 is descriptive. Estimating the college mean is inferential.
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3. Classify board code, number of siblings, rank, Celsius temperature and height by scale.
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Board code: nominal. Sibling count: ratio. Rank: ordinal. Celsius: interval. Height: ratio.
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4. We record rainfall each day for a year. Is that cross-sectional?
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It is a time series. Preserve chronological order.
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5. A height column contains 170 cm and 1.65 m. What must be fixed?
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Convert to a common unit: 170 cm and 165 cm, for example.
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6. A spreadsheet is sorted only by moving the marks column. What can go wrong?
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Marks can become attached to the wrong student. Sort the whole table together.
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7. Is a mean of board codes useful?
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No. Board codes label categories; their average does not describe a meaningful board.
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8. Can a table with marks but no study-time column answer how study time relates to marks?
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No. The required variable was not recorded.
More practice: apply what you learned
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9. A city wants to know the travel time of all bus passengers this month, but interviews 200 passengers. Identify population and sample.
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Population: the bus passengers covered by the question this month. Sample: the 200 interviewed passengers. Place, time and eligibility define the population.
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10. A report says “12 of our 30 respondents prefer online classes.” Is this descriptive or inferential?
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Descriptive. It reports the responses actually observed. Saying the same proportion applies to every student would go beyond these data and be inferential.
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11. A researcher records every household in a village. Is this a sample survey or a census of those households?
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A census. Every household in the defined village population is included. A summary of their recorded data is still descriptive statistics.
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12. A file has 18 data rows and 5 columns. The first row above them contains headings. How many cases are there?
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18 cases, assuming one case per data row. The heading row names the variables and is not another case. There are 5 recorded columns.
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13. A table has one row per cricket match, with date, venue and runs scored. What is a case?
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One match. Date, venue and runs scored are recorded variables. A case need not be a person.
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14. Classify school name, shoe size, monthly rent and number of pets as categorical or numerical.
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School name is categorical. Shoe size, monthly rent and number of pets are numerical. Shoe size has a numerical scale; do not confuse it with ordered labels such as Small, Medium and Large.
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15. A survey uses 1 = bus, 2 = bicycle and 3 = walk. Can the mean code describe an average transport method?
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No. The values are nominal category codes. An average such as 1.8 does not name a meaningful transport method. Count the categories instead.
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16. Classify service ratings Poor, Fair, Good and Excellent by measurement scale. Can we assume equal gaps?
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Ordinal: the categories have an order. We cannot assume the improvement from Poor to Fair equals the improvement from Good to Excellent.
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17. A room changes from 10°C to 20°C. What numerical comparison is valid?
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The temperature increases by 10°C. It is not valid to say that 20°C is twice as hot in a ratio sense, because the Celsius zero is arbitrary.
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18. Classify elapsed time in seconds and finish position in a race.
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Elapsed time is ratio-scaled: equal time units and a meaningful zero. Finish position is ordinal: first, second and third give order but not the gaps in running time.
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19. Heights of different students are measured on Monday. Is this a time series just because Monday is mentioned?
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No. It is a snapshot across students at about one time. A date in the description does not by itself make data a time series.
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20. A column contains 2 meters and 150 centimeters. Express both in centimeters before comparison.
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2 meters = 200 centimeters. The comparable values are 200 cm and 150 cm. Keep one unit in the column heading.
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21. After filtering a dataset from 100 people to 25 people, how many cases are visible? Does the filter change their recorded values?
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25 cases are visible. A filter selects matching rows; it does not change the values recorded for those rows.
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22. A file has “State”, “state” and “State ” in its Board column. What should be checked?
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These may be the same board label with differences in capitalization or spaces. Standardize them carefully so one category is not accidentally counted as three.
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23. A table contains age and marks but no attendance information. Can it answer whether attendance is related to marks?
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No. Attendance was not recorded. You need the required variables paired for the same students before exploring their relationship.
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24. We ask 15 friends and estimate the preferences of every teenager in India. What makes that conclusion weak?
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The sample is small and selected from friends, who may share similar backgrounds or preferences. It is not automatically representative of all Indian teenagers.
Ready to move on?
Explain each answer in your own words. If you cannot explain the denominator, category order or measurement scale, revisit that lesson before continuing.