Question: 2 (a) Mika counts the number of letters in each of the 61 words in a paragraph. Some of his results are shown in the table and bar chart.
Number of letters
1 2 3 4 5 6
Frequency
7 12 15 5
Frequency
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Number of letters
Complete the table and the bar chart. Write down the mode.
Graph: a bar chart at center showing frequency against number of letters, with bars at 17, 212, 315, 415, 5F , 65; position_hint=center
1. **State the problem:** Mika counted the number of letters in each of the 61 words in a paragraph. We have partial frequency data for words with 1 to 6 letters and need to complete the table and bar chart, then find the mode.
2. **Given data:**
- Number of letters: $1, 2, 3, 4, 5, 6$
- Frequencies: $7, 12, 15, 5$ (incomplete, missing frequency for 5 letters)
3. **Calculate the missing frequency:**
- Total words counted: $61$
- Sum of known frequencies: $7 + 12 + 15 + 5 = 39$
- Let frequency for 5 letters be $x$
- Equation: $$7 + 12 + 15 + 5 + x = 61$$
- Simplify: $$39 + x = 61$$
- Solve for $x$: $$x = 61 - 39 = 22$$
4. **Complete frequency table:**
| Number of letters | Frequency |
|-------------------|-----------|
| 1 | 7 |
| 2 | 12 |
| 3 | 15 |
| 4 | 5 |
| 5 | 22 |
| 6 | 5 |
5. **Identify the mode:**
- The mode is the number of letters with the highest frequency.
- Frequencies: $7, 12, 15, 5, 22, 5$
- Highest frequency is $22$ for $5$ letters.
- Therefore, the mode is **5 letters**.
6. **Bar chart completion:**
- Bars heights correspond to frequencies: 1 letter = 7, 2 letters = 12, 3 letters = 15, 4 letters = 5, 5 letters = 22, 6 letters = 5.
**Final answer:**
- Missing frequency for 5 letters is $22$.
- Mode is $5$ letters.