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Data: 5,8,8,10,12,15,50. Mean?
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All Flashcards in Topic 6.7
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6.7.120 cards
Data: 5,8,8,10,12,15,50. Mean?
(5+8+8+10+12+15+50) ÷ 7 = 108 ÷ 7 = 15.4
15.4
Mean = total ÷ count (affected by ___). Median = middle (___). Mode = most frequent.
Outliers; not affected by outliers.
Outliers; unaffected
What are measures of central tendency?
Ways to find the 'middle' or 'typical' value — mean, median and mode.
Middle value: mean, median, mode
When to use mean?
Evenly spread data with no extreme outliers — the standard 'average'.
No outliers
Choose the right measure for the data — ___ matter!
Outliers — they determine whether mean or median is more appropriate.
Outliers
When to use median?
When outliers could distort the average — e.g. wages, house prices.
Outliers present
Mean formula?
Add up all values ÷ number of values. Uses every data point but distorted by outliers.
Total ÷ count
Data: 5,8,8,10,12,15,50. Median?
10 — the 4th value (middle of 7 ordered values).
10
Always show your ___ in calculations
Working — method marks available even if answer is wrong.
Working
Data: 5,8,8,10,12,15,50. Mode?
8 — appears twice, more than any other value.
8
When to use mode?
Finding the most popular item — e.g. best-selling shoe size or product.
Most popular
What is the median?
Middle value when data is ordered. Not affected by outliers — good for skewed data.
Middle when ordered
Mean = add and divide. Median = ___. Mode = ___
Middle of ordered list; most frequent.
Middle; most frequent
Quick: Outlier present → use ___
Median instead of mean.
Median
The mean (15.4) is pulled up by the outlier (50). Better measure?
Median (10) — more representative of the typical value.
Median
What is the mode?
Most frequent value. Can have no mode, one, or multiple. Useful for popularity.
Most common
For salary data, ___ is usually better than mean
Median — a few very high salaries pull the mean up, giving a misleading average.
Median
Mean is distorted by ___ but median is not
Outliers (extreme values) — mean gets pulled toward them.
Outliers
If data has an obvious outlier, comment on ___ and suggest ___
How the mean is distorted; the median as a better measure.
Mean distorted → use median
Quick: Most popular item → use ___
Mode.
Mode
6.7.215 cards
Range = highest − lowest (simple but ___). SD = average distance from mean (more ___)
Limited; reliable.
Limited vs reliable
Range formula?
Highest value − Lowest value. Simple but only uses two data points.
Highest − lowest
Low dispersion in sales means ___
Consistent, predictable revenue — easier to plan and budget.
Predictable + easy to plan
Low dispersion = consistent. High dispersion = ___
Variable and risky — harder to predict and manage.
Variable + risky
What does standard deviation measure?
How far each value is from the mean on average — uses ALL data points.
Average distance from mean
High dispersion in sales means ___
Volatile, unpredictable revenue — harder to forecast and manage cash flow.
Volatile + hard to forecast
You ___ SD in exams, you don't ___ it
Interpret; calculate.
Interpret
Low dispersion in quality means ___
Consistent products — good for reputation and customer trust.
Consistent + trust
Low SD means ___; High SD means ___
Low = data clustered close to mean (consistent). High = data spread widely (variable).
Clustered vs spread
Two shops: both average $10k/week. Shop A: $9k-$11k. Shop B: $3k-$17k. Which is easier to manage?
Shop A — low spread means predictable, easier to plan staffing and stock.
Shop A (low spread)
Range is limited because ___
It only uses two values (highest and lowest) — ignores everything in between and distorted by outliers.
Only 2 values
Quick: Businesses prefer low dispersion because ___
It means consistency — easier to plan, budget and maintain quality.
Consistency
Businesses prefer ___ dispersion in sales and quality
Low — consistency is easier to manage and builds customer confidence.
Low
You won't need to ___ SD in the exam — just ___
Calculate; understand what high or low SD means for the business.
Interpret, not calculate
Quick: SD uses ___ data points; range uses only ___
All; two.
All vs two
6.7.320 cards
Statistics: identify trends, compare, forecast, spot problems, ___
Support data-backed decisions.
Support decisions
You must be able to CONSTRUCT ___ and ___ in exams
Bar charts (simple + stacked) and pie charts — not just read them.
Bar charts + pie charts
Name four ways statistics help managers
Identify trends, compare performance, forecast future, spot problems, support data-backed decisions.
Trends, compare, forecast, problems
Three limitations of using statistics?
Small/biased samples can mislead; shows WHAT not WHY; past ≠ future; can be cherry-picked; ignores qualitative.
Sample + what not why + past
Statistics show WHAT happened, not ___
WHY — numbers don't explain the reasons behind the data.
Why
High average satisfaction (4.2/5) but high SD means ___
Inconsistency — some customers love it, others hate it. The variation is the real problem.
Inconsistency is the problem
Must construct: bar charts (simple + stacked) and ___
Pie charts — calculate degrees and draw accurately.
Pie charts
Pie chart: calculate degrees formula?
(Value ÷ Total) × 360 degrees.
Value/total × 360
Limitations: past ≠ future, can mislead, ignores ___
Qualitative factors — always combine quant with qual judgement.
Qualitative
Bar chart must include: title, labelled axes, ___, ___
Equal width bars, drawn to scale, key/legend if multiple categories.
Equal bars + scale + key
Past data doesn't guarantee ___
Future results — trends can change unexpectedly.
Future
Data-backed arguments are more convincing than ___
Gut feelings — statistics provide objective evidence for decisions.
Gut feelings
Numbers can be ___ to support a preferred conclusion
Manipulated or cherry-picked — selective use of data is misleading.
Cherry-picked
Not to scale = maximum ___ out of 4 marks
3 — scale matters for accuracy marks.
3/4
Statistics help spot problems by showing ___
Unusually high or low figures that signal something needs attention.
Unusual figures
Bar charts: labelled axes, to scale, equal width, ___
Key if needed, clear title.
Key + title
Statistics support ___ based on past data
Forecasting — predicting future demand, revenue or costs using historical trends.
Forecasting
Statistics are a tool, not the answer — combine with ___
Context, judgement and qualitative factors.
Context + judgement + qualitative
Stacked bar chart: bars divided into ___ showing subcategories
Segments — each segment shows a different subcategory, total height = total value.
Segments
Quick: Pie chart degrees = value ÷ total × ___
360.
360
Topic 6.7 study notes
Full notes & explanations for Descriptive statistics
BM exam skills
Paper structures, command terms & tips
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