Business and statistics
Statistics is the science of collecting, organising, showing and understanding data. A business cannot read thousands of bills one by one, so it uses statistics to find the main message.
- Sales: which product sells most, which month is best.
- Customers: how many, how old, what do they like.
- Cost control: where did we spend more than planned.
Steps: collect data → tally → make a table → draw a graph → calculate summary numbers → decide.
Tables, graphs and analysing information
Tally marks: one stroke per item, the fifth stroke crosses the four. A frequency table lists each category with its count.
Graphs:
- Bar graph: compare separate categories.
- Line graph: change over time.
- Pie chart: parts of a whole (percentages).
Use a title, labels and units. Start bars at zero.
Summary numbers:
- Mean = sum of values / number of values.
- Median = middle value after sorting (if two are in the middle, take their mean).
- Mode = value that appears most often.
- Range = biggest - smallest.
- Percentage share = part / total x 100. Percentage change = (new - old) / old x 100.
Finding and solving problems
Numbers help you notice what is wrong, then fix it.
- Find: compare with the average, the target or last month. A bar far below is a clue.
- Define: say the problem clearly in one sentence.
- Look for causes: ask "why?" several times; collect more data.
- Try solutions: pick one idea, test it small.
- Check: count again. Did the number improve? Keep it, or try another idea.
Be careful: a pattern does not always show the cause, and a small sample can mislead.
Try it: your own survey
Ask 20 people their favourite fruit. Make tally marks, a frequency table and a bar graph. Find the mean count, the mode and the percentage for the top fruit. Which fruit is far below the average? Write one possible reason and one way to check it.
Key formulas and definitions
- Mean = sum / number of values
- Median = middle value of the sorted list
- Mode = most frequent value
- Range = largest - smallest
- Percentage share = part / total x 100
- Percentage change = (new - old) / old x 100
Worked examples
1. Tally for Cricket shows one group of five and two more strokes. What is the frequency?
5 + 2 = 7.
2. Daily sales are 12, 15, 9 and 14. Find the mean.
Sum = 50. Mean = 50 / 4 = 12.5.
3. Find the median of 3, 7, 5, 9, 11.
Sort: 3, 5, 7, 9, 11. The middle value is 7.
4. Find the mode of 4, 6, 6, 7, 9, 6, 4.
6 appears three times, more than any other value. Mode = 6.
5. Kabaddi got 9 of the 20 votes. What is its percentage share?
9 / 20 x 100 = 45%.
6. Sales rose from 80 to 100 units. Find the percentage change.
(100 - 80) / 80 x 100 = 25% increase.
Common mistakes
- Putting the fifth tally stroke beside the others instead of across them. This makes counting slow.
- Starting a bar graph axis above zero, which makes small gaps look big.
- Taking mean, median and mode as the same thing.
- Using percentage change with the new value in the denominator. Divide by the OLD value.