Below is a frequency distribution of achievement scores for a sample of at-risk youths. Use the
information to answer questions 1a through 1c. (NOTE THAT “f” IS THE NUMBER OF TIMES A
SCORE APPEARS IN THE DISTRIBUTION. FOR EXAMPLE, IN THE DISTRIBUTION BELOW,
THE SCORE OF “40” APPEARED 10 TIMES, THE SCORE OF “38” ALSO APPEARS 10 TIMES,
AND SO ON).
Scores f
__________________________
40 10
38 10
36 13
34 7
32 11
30 9
28 3
26 12
25 3
22 6
_________________________  Calculate the mean in statistics

To calculate the mean (average) of a frequency distribution, we need to multiply each score by its corresponding frequency, sum these products, and then divide by the total number of observations.

The formula for the mean (\(\bar{x}\)) is:

\[
\bar{x} = \frac{\sum (x_i \cdot f_i)}{N}
\]

where:
- \(x_i\) is each individual score,
- \(f_i\) is the frequency of each score,
- \(N\) is the total number of observations.

### Step-by-Step Calculation

1. **Multiply each score by its frequency:**

\[
\text{Sum of } (x_i \cdot f_i) = (40 \times 10) + (38 \times 10) + (36 \times 13) + (34 \times 7) + (32 \times 11) + (30 \times 9) + (28 \times 3) + (26 \times 12) + (25 \times 3) + (22 \times 6)
\]

2. **Calculate the total number of observations (N):**

\[
N = 10 + 10 + 13 + 7 + 11 + 9 + 3 + 12 + 3 + 6
\]

Let me compute these values for you.The mean (average) score for the distribution is approximately **32.27**.

Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How is the median score calculated for this dataset?
2. What is the mode of this frequency distribution?
3. How do you compute the variance and standard deviation for this dataset?
4. How would the mean change if an additional score was added to the dataset?
5. What are the implications of this mean score for the at-risk youth population?

**Tip:** The mean gives a central tendency of the data, but considering other measures like the median and mode can provide a fuller understanding of the distribution.

Below is a frequency distribution of achievement scores for a sample of at-risk youths. Use the information to answer questions 1a through 1c. Calculate the mean in statistics.

Learn how to calculate the mean from a frequency distribution of achievement scores for at-risk youths. This problem covers key concepts in descriptive statistics, including the use of the mean formula in a frequency distribution context. Suitable for students in Grades 9-12.

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