DataFrequency

50 - 54

1

55 - 59

1

60 - 64

3

65 - 69

6

70 - 74

6

75 - 79

8

80 - 84

15

85 - 89

18

90 - 94

10


mean = 

To calculate the **mean** (average) of the given data, follow these steps:

1. **Find the midpoint** of each class interval (e.g., 50-54, 55-59, etc.).
2. **Multiply** each midpoint by the frequency of that class interval.
3. **Sum** the products from step 2.
4. **Divide** the sum by the total frequency to find the mean.

### Step 1: Calculate midpoints of each class interval
For each class interval, the midpoint is the average of the lower and upper bounds:

\[
\text{Midpoint} = \frac{\text{Lower bound} + \text{Upper bound}}{2}
\]

- \( \frac{50 + 54}{2} = 52 \)
- \( \frac{55 + 59}{2} = 57 \)
- \( \frac{60 + 64}{2} = 62 \)
- \( \frac{65 + 69}{2} = 67 \)
- \( \frac{70 + 74}{2} = 72 \)
- \( \frac{75 + 79}{2} = 77 \)
- \( \frac{80 + 84}{2} = 82 \)
- \( \frac{85 + 89}{2} = 87 \)
- \( \frac{90 + 94}{2} = 92 \)

### Step 2: Multiply midpoints by frequencies
Now multiply each midpoint by its corresponding frequency:

- \( 52 \times 1 = 52 \)
- \( 57 \times 1 = 57 \)
- \( 62 \times 3 = 186 \)
- \( 67 \times 6 = 402 \)
- \( 72 \times 6 = 432 \)
- \( 77 \times 8 = 616 \)
- \( 82 \times 15 = 1230 \)
- \( 87 \times 18 = 1566 \)
- \( 92 \times 10 = 920 \)

### Step 3: Sum of the products
\[
52 + 57 + 186 + 402 + 432 + 616 + 1230 + 1566 + 920 = 5461
\]

### Step 4: Total frequency
The total frequency is:
\[
1 + 1 + 3 + 6 + 6 + 8 +

DataFrequency
50 - 54
1
55 - 59
1
60 - 64
3
65 - 69
6
70 - 74
6
75 - 79
8
80 - 84
15
85 - 89
18
90 - 94
10

mean = 

Learn how to calculate the mean of grouped data with frequencies using midpoints and frequencies. This statistical method is ideal for understanding grouped data distributions. Includes a step-by-step breakdown of calculations for the given frequency data set, covering intervals 50-94.

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