
89	88	87	70	89	73
70	72	94	93	78	79
71	89	78	90	75	80
84	88	89	72	90	87
78	70	76	75	75	78
(a) Complete the frequency distribution for the data. Give relative frequencies as a decimal rounded to 2 decimal places.

Age	Frequency	Relative Frequency
70-74	
75-79	
80-84	
85-89	
90-94	


To complete the frequency distribution, we need to:

1. Count how many numbers fall within each age range (70-74, 75-79, etc.).
2. Calculate the total number of data points.
3. Compute the relative frequency by dividing each frequency by the total number of data points, then round the result to 2 decimal places.

### Data:
89, 88, 87, 70, 89, 73  
70, 72, 94, 93, 78, 79  
71, 89, 78, 90, 75, 80  
84, 88, 89, 72, 90, 87  
78, 70, 76, 75, 75, 78

### Step 1: Count the Frequency
Let's count how many numbers fall into each range:

- **70-74**: 70, 73, 70, 72, 71, 72, 70 → 7 numbers
- **75-79**: 78, 79, 78, 75, 78, 75, 78 → 7 numbers
- **80-84**: 80, 84 → 2 numbers
- **85-89**: 89, 88, 87, 89, 89, 89, 88, 89, 87 → 9 numbers
- **90-94**: 94, 93, 90, 90 → 4 numbers

### Step 2: Calculate Total Number of Data Points
Total data points = 7 + 7 + 2 + 9 + 4 = 29

### Step 3: Calculate Relative Frequency
Relative frequency is calculated as:
\[
\text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Data Points}} \text{ rounded to 2 decimal places}
\]

- **70-74**: \( \frac{7}{29} = 0.24 \)
- **75-79**: \( \frac{7}{29} = 0.24 \)
- **80-84**: \( \frac{2}{29} = 0.07 \)
- **85-89**: \( \frac{9}{29} = 0.31 \)
- **90-94**: \( \frac{4}{29} = 0.14 \)

### Final Frequency Distribution Table

| Age    | Frequency | Relative Frequency |
|--------|-----------|--------------------|
| 70-74  | 7         | 0.24               |
| 75-79  | 7         | 0.24               |
| 80-84  | 2         | 0.07               |
| 85-89  | 9         | 0.31               |
| 90-94  | 4         | 0.14               |

Would you like any further details or explanations?

Here are 5 related questions to expand on this topic:
1. How can relative frequencies be represented visually?
2. What is the cumulative frequency and how is it calculated?
3. How do you calculate percentages from relative frequencies?
4. Why is it important to round relative frequencies in data analysis?
5. What are other ways to organize and present frequency data?

**Tip**: Always check that the sum of relative frequencies equals 1 (or very close due to rounding).

Complete the frequency distribution for the data. Give relative frequencies as a decimal rounded to 2 decimal places. Data: 89 88 87 70 89 73 70 72 94 93 78 79 71 89 78 90 75 80 84 88 89 72 90 87 78 70 76 75 75 78

Learn how to complete a frequency distribution with relative frequencies rounded to 2 decimal places. The data set includes values ranging from 70 to 94, categorized into age ranges of 70-74, 75-79, 80-84, 85-89, and 90-94. This tutorial is ideal for students in Grades 9-12, focusing on statistics and data analysis.

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