Centre, spread and data displays · Core
הוצג| English | משמעות |
|---|---|
| range/reɪndʒ/ | טווח |
Can one average tell the whole story?
- Two groups have the same median but different spread. One summary cannot describe both location and consistency.
- This lesson studies range 极差: The maximum observed value minus the minimum observed value.
The method
- The mean is total divided by count.
- The median is the central value after sorting.
- The range is maximum minus minimum.
- Use frequency tables, bar charts and suitable comparisons.
For 2, 4, 4, 6, 9, why is the median 4 but the mean 5?
רמת קושי 1/5 · 100 מטבעות + בונוס קטן בהשלמה הראשונה היום
Sorted, the central value is 4. The mean is 25/5=5 because the value 9 pulls the total up. They measure centre differently.
A worked case
For 2,4,4,6,9, total=25 and count=5, so mean=5. The central value is 4, so median=4. The range is 9-2=7. Explain both a typical value and the spread.
Centre, spread and data displays
The mean is total divided by count
Choose a centre and a spread measure for the worked observations.
Find the range of 2,4,4,6,9.
רמת קושי 2/5 · 140 מטבעות + בונוס קטן בהשלמה הראשונה היום
Range=maximum-minimum=9-2=7.
Where it goes wrong
- The tallest histogram bar need not contain the most observations.
- A grouped mean is an estimate.
- Correlation does not prove causation, and extrapolation extends beyond the observed range.
Not true: The mean of a list must be one of its observed values. With unequal class widths the height is frequency density; frequency is the area of the bar.
Find the mean of 2,4,4,6,9.
רמת קושי 2/5 · 140 מטבעות + בונוס קטן בהשלמה הראשונה היום
The total is 25 across five observations: mean=25/5=5.
With unequal class widths the height is frequency density.
רמת קושי 1/5 · 100 מטבעות + בונוס קטן בהשלמה הראשונה היום
True. With unequal class widths the height is frequency density; frequency is the area of the bar.
Applying it
- A bar chart uses separate bars for categories.
- Unequal-class-width histograms and formal density calculations are outside this Foundation/Core lesson.
Find the median of 2,4,4,6,9.
רמת קושי 2/5 · 140 מטבעות + בונוס קטן בהשלמה הראשונה היום
The sorted list is 2,4,4,6,9. Its third observation is 4.
Match each measure to its value for 2, 4, 4, 6, 9.
רמת קושי 2/5 · 140 מטבעות + בונוס קטן בהשלמה הראשונה היום
Mean=25/5, median is the third of five sorted values, and range=9-2.
In your course
- OxfordAQA International GCSE Mathematics (9260), Core tier, specification section 3.4.
- Every paper allows a calculator, but method marks still need the expression or equation written before its value.
- Range: The maximum observed value minus the minimum observed value.
- The mean is total divided by count.
- Watch for: the tallest histogram bar need not contain the most observations.
Write from a mean of 9 and a median of 8
- The values are 1, 6, 8, 11 and 19.
- Find the mean, the median and the range.
For the values 1, 6, 8, 11 and 19, what are the mean, the median and the range?
45 divided by 5 is 9. The third value in the ordered list is 8.
What is the median?
רמת קושי 1/5 · 100 מטבעות + בונוס קטן בהשלמה הראשונה היום
The ordered middle value is 8. The mean is 9. Other options — 4 (the lesson median of 2, 4, 4, 6, 9); 9 (the mean of this list).