Data analysis and evidence

A count of 4 passes a form's whole-number rule, but the trusted original record says 9. Which value should be treated as an unresolved data-quality issue before analysis?

Rule acceptance and agreement with the trusted record are separate

Keep a usable record before calculating

Keep an unchanged copy of source data and record what each row, field and unit means

Record the source, collection period and definitions. Document any correction rather than silently replacing inconvenient observations

Missing data are not automatically zero. Repeated values may be genuine separate observations rather than accidental duplicates

Keep observations separate from interpretations so another reader can check the path from record to claim

Do not manufacture a missing observation

Trace a graphic back to its evidence

An online graphic states that an average increased

It gives no original data source, collection dates, observation group or definition of average

What is needed before using this graphic as evidence for a statistical claim?

Trace the graphic to the original data or report

Check what observations were included and when they were collected

Identify units, collection method and whether average means mean or median

Use the claim only with its supported meaning and limitations

Identify the source relationship

Use the mathematical method appropriate to the question

Use the previously taught meanings of mean, median, mode and range. They answer different questions about centre, frequency and spread

Mean uses the total and observation count; median uses ordered middle positions; mode uses frequency under the stated convention; range is maximum minus minimum

A tool can calculate a summary correctly from the wrong selected cells. Check the records, range, units and repeated observations as well as the arithmetic

Give each summary in the exact response form requested; do not round an exact calculation unless instructed

Calculate from a complete supplied record

Illustrative data record the number of leaves on each seedling

These are counts of individual leaves. Each entry is one observation

Data: 2, 4, 4, 6, 9

Calculate the four requested summaries of this data set

Give exact values as whole numbers, terminating decimals or simplified fractions. Do not round

Use every observation in the total, including repeated values

Add the 5 displayed values

There are 5 values, so divide the sum by 5

The mean is the equal-share value for this total and number of observations

Order the observations and locate the middle position or positions

Order the data: 2, 4, 4, 6, 9

There are 5 values, so use position 3

The median depends on ordered position, not the original recording order

Count every occurrence, including repeats

2 occurs 1 time

4 occurs 2 times

6 occurs 1 time

9 occurs 1 time

The greatest frequency is 2, so the mode is 4

A mode is a data value, not its frequency

Use the smallest and largest observed values

The largest value is 9 and the smallest value is 2

The range describes the distance between extremes, not a central value

Keep the whole record and the requested measures

A display is a representation, not a replacement record

Check a chart's variables, units, scale, key and observation count against its source record

A rounded overview can reveal distribution shape while losing exact values. Calculate exact summaries from the original table when the task says to do so

A dot plot shows the distribution of values, not necessarily their time order. Do not infer a day-by-day trend from positions that have been sorted or grouped

Read the collection dates, publication details and stated limits before using a published record to support a claim

Two displays should preserve the same observations

Use the exact published table, not rounded plot positions

Published secondary data: Australian marriages by date of occurrence in January 2023

One observation is one date’s published marriage count, not one individual marriage

Source: Australian Bureau of Statistics, Marriages and Divorces, Australia, 2023; released 16 August 2024

https://www.abs.gov.au/statistics/people/people-and-communities/marriages-and-divorces-australia/2023

Accessed 25 October 2026; Commonwealth of Australia, CC BY 4.0; table and plot redrawn from the published snapshot

These published occurrence counts include registrations received in 2024. They are not a claim of complete eventual counts

For a readable overview only, the dot plot rounds each daily count to the nearest hundred. Keep the original table for every exact calculation

The dot plot shows the distribution of rounded daily counts, not their time order. Its grouped positions are approximate; different exact counts can share a rounded position. Calculate all summaries, including modes, from the exact table

Calculate each requested exact summary from the published record

Keep exact integers, terminating decimals or simplified fractions without rounding

Supplied dates: order the 7 daily counts as 61, 70, 117, 146, 202, 366, 818

Their total is 1780. Divide by 7 dates to obtain mean daily count \(\frac{1780}{7}\)

Position 4 gives median 146

Maximum 818 minus minimum 61 gives range 757

All supplied counts are different, so there is no mode under the convention used here

The large upper values extend the distribution above the main group; a mean alone does not describe that shape

The conclusions describe only the dates supplied in this published snapshot, not the whole year or a cause of the pattern

Published secondary data: Australian marriages by date of occurrence in January 2023 One observation is one date’s published marriage count, not one individual marriage Source: Australian Bureau of Statistics, Marriages and Divorces, Australia, 2023; released 16 August 2024 https://www.abs.gov.au/statistics/people/people-and-communities/marriages-and-divorces-australia/2023 Accessed 25 October 2026; Commonwealth of Australia, CC BY 4.0; table and plot redrawn from the published snapshot These published occurrence counts include registrations received in 2024. They are not a claim of complete eventual counts Choose a date from 8 to 14 January. Predict its nearest-hundred display value, then compare the exact and rounded readouts. The selector does not change the original count

Both 9 and 10 January round to 100 in this overview. What follows about their exact counts?

Read a second supplied record with its source limits

Report what the evidence actually supports

State which observations, place and period a comparison concerns

A difference in a median is not a statement about every individual observation. A difference between groups does not by itself establish its cause

Keep the supported result and its limitations together. A polished chart does not remove a sampling, recording or comparison problem

A proposed prediction needs an explicit reason for extending a pattern beyond the observed data; it is not guaranteed by the chart

Keep a conclusion within the observed scope

A comparison does not establish its cause

Keep only information required by the task

A data-processing task should have a clear purpose before fields are collected or shared

Use synthetic data for these activities. Do not enter real personal details, account credentials or private records

For a classroom investigation, follow the teacher's collection, access and sharing rules

Preserve useful evidence without unnecessary identifiers

A task must import a numeric table, filter rows, calculate totals and make a labelled chart. Tool A explicitly supports those four operations. Tool B only crops and annotates pictures. Tool C only stores plain text and offers no calculations or charts. Which tool meets all stated requirements?

Compare every required operation with the capabilities actually given

Keep the method, result and limitation together

Separate practical evidence from these automatic checks

Teacher-reviewed practical task, not automatically assessed here

Using an approved spreadsheet tool, recreate this synthetic count table and preserve an unchanged original sheet

Add a correctly referenced two-day total for each team, copy the formula down, and verify every result against the original counts

Create a labelled chart for one clearly stated comparison. Check its variables, units, scale and values against the table, then explain the limited conclusion it supports

Record the tool, formulas, changes and checks actually used. Submit that record through the teacher's approved process, not as personal data in this activity

Keep the path from records to claims visible

Keep source definitions, original observations and a record of justified corrections

Apply the requested mathematical methods to the exact data, and explain any display rounding or grouping

Limit claims to the evidence and retain uncertainty about causes, generalisation and predictions

Choose tools and fields for the stated task, and keep a record of the formulas, charts and checks actually used