Question: QUESTION ONE: DATA PRESENTATION AND INTERPRETATION (6 MARKS)
A supermarket in Kira Municipality recorded the following number of customers visiting its outlet over 20 randomly selected trading days:
125, 142, 138, 155, 167, 149, 132, 175, 160, 145, 151, 139, 182, 170, 158, 147, 135, 190, 163, 156
Required:
a) Construct a suitable frequency distribution using five appropriate class intervals. (2 marks)
b) Present the data using an appropriate graph or chart. Give a reason for your choice of presentation technique. (2 marks)
c) Write a brief interpretation of what the presentation tells management about customer traffic. (1 mark)
d) Explain two limitations of presenting quantitative data only in a table. (1 mark)
1. **State the problem:** We have 20 customer counts over 20 days and need to create a frequency distribution with 5 class intervals, present the data graphically, interpret it, and explain limitations of tables.
2. **Find the range:** Maximum value = $190$, minimum value = $125$.
3. **Calculate class width:**
$$\text{Class width} = \frac{190 - 125}{5} = \frac{65}{5} = 13$$
4. **Construct class intervals:** Starting from 125, intervals of width 13:
- $125 - 137$
- $138 - 150$
- $151 - 163$
- $164 - 176$
- $177 - 189$
5. **Tally frequencies:**
- $125 - 137$: 125, 132, 135 = 3
- $138 - 150$: 138, 139, 142, 145, 147, 149 = 6
- $151 - 163$: 151, 155, 156, 158, 160, 163 = 6
- $164 - 176$: 167, 170, 175 = 3
- $177 - 189$: 182, 190 = 2
6. **Frequency distribution table:**
| Class Interval | Frequency |
|----------------|-----------|
| 125 - 137 | 3 |
| 138 - 150 | 6 |
| 151 - 163 | 6 |
| 164 - 176 | 3 |
| 177 - 189 | 2 |
7. **Graphical presentation:** A histogram or bar chart is appropriate because it shows frequency distribution clearly for grouped data.
8. **Interpretation:** Most customer visits fall between $138$ and $163$, indicating moderate to high traffic on most days.
9. **Limitations of tables:**
- Tables can be hard to interpret quickly compared to graphs.
- They do not show trends or patterns visually.
Final answer: Frequency distribution constructed, histogram recommended, interpretation and limitations explained.