Unit 1 Assessment | Mathematics Project

Practice, not certification. This is an ungraded assessment with no timer, identity requirement, server-side score collection, or claim of educational accreditation. For questions involving real studies, use the stated assumptions.

Question 1 · The population is not the sample

A city interviews 400 of its 20,000 residents. The target is citywide transit opinion. What is the population?

The 400 selected peopleAll 20,000 city residentsOnly people who respondEvery resident of the country

Question 2 · A parameter or a statistic?

The mean study time calculated from 150 sampled students is which of these?

The population parameterA sample statisticA measurement scaleA sampling frame

Question 3 · Digits can still be labels

A student's postal ZIP code is best treated as which variable type?

A nominal categorical identifierA continuous ratio variableAn interval-scale distanceA count of students

Question 4 · Resistant center

Which statistic stays at 50 if data 40, 45, 50, 55, 60 change to 40, 45, 50, 55, 600?

MeanRangeMedianStandard deviation

Question 5 · A sample-standard-deviation detail

Why does the usual sample variance use n−1 in the denominator?

To make every variance smallerTo correct the estimated population variance under standard i.i.d. assumptionsTo remove outliersTo force zero variance

Question 6 · Bin choice versus data

Changing a histogram from 5 to 20 equal-width bins while holding the raw observations fixed can change what?

The observationsThe sample meanThe histogram's apparent shapeThe actual sample median

Question 7 · Quartiles require a convention

For the ordered values 2,4,6,8,10, what is the type-7 interpolated IQR?

2468

Question 8 · Beware the truncated bar chart

A bar chart displaying 98 and 102 uses a vertical axis beginning at 95. What is the primary concern?

The original numbers are necessarily fakeTruncated bar baselines can exaggerate visual differencesAll line graphs must start at zeroPercentages may never appear on a bar chart

Question 9 · Sampling versus assigning

Randomly assigning volunteers to two treatments primarily helps with which goal?

Guaranteeing population representativenessCausal comparison under the experimental designMaking all participants identicalPreventing all missing values

Question 10 · A blank is not a zero

A temperature record is missing on one day. What should a reproducible analysis generally avoid?

Documenting the missing valueInvestigating the instrument and missingnessSilently replacing it with zeroReporting the number of complete observations

Question 11 · Correlation is not enough

Pearson's r is near zero. Which inference is justified?

The variables are independentNo nonlinear relation is possibleA strong curved relationship may still existAt least one variable is constant

Question 12 · The research needs a source

Which submission is most reproducible?

An attractive graphic with no metadataA chart plus an unexplained p-valueRaw numbers copied without unitsA documented source, code, units, transformations and missingness