Question

The following table shows the ACT scores of a select group of students and how frequent certain scores were among the student population.
ACT Score
36 34 27 22 21 20 19 18 17
Frequently
1 1 4 6 7 3 7 3 4

Answer 1

To better understand the data you've provided, we can summarize the frequency of the ACT scores and potentially calculate some statistics if needed. Here is the information in a formatted way:

| ACT Score | Frequency |
|-----------|-----------|
| 36 | 1 |
| 34 | 1 |
| 27 | 4 |
| 22 | 6 |
| 21 | 7 |
| 20 | 3 |
| 19 | 7 |
| 18 | 3 |
| 17 | 4 |

### Total Frequency
We can find the total number of students by summing the frequencies:

\[
\text{Total Frequency} = 1 + 1 + 4 + 6 + 7 + 3 + 7 + 3 + 4 = 36
\]

### Mean (Average) ACT Score
To find the mean ACT score, we calculate the sum of the products of each score and its frequency, and then divide by the total frequency.

\[
\text{Mean} = \frac{(36 \times 1) + (34 \times 1) + (27 \times 4) + (22 \times 6) + (21 \times 7) + (20 \times 3) + (19 \times 7) + (18 \times 3) + (17 \times 4)}{36}
\]

Calculating the numerator:

\[
= 36 + 34 + (27 \times 4) + (22 \times 6) + (21 \times 7) + (20 \times 3) + (19 \times 7) + (18 \times 3) + (17 \times 4)
\]
\[
= 36 + 34 + 108 + 132 + 147 + 60 + 133 + 54 + 68 = 732
\]

Now, divide by the total frequency:

\[
\text{Mean} = \frac{732}{36} = 20.33
\]

### Median

To find the median, we need to list out the scores based on their frequencies:

- 36, 34
- 27, 27, 27, 27
- 22, 22, 22, 22, 22, 22
- 21, 21, 21, 21, 21, 21, 21
- 20, 20, 20
- 19, 19, 19, 19, 19, 19, 19
- 18, 18, 18
- 17, 17, 17, 17

Arranging this gives a total of 36 scores:

- 36, 34, 27, 27, 27, 27, 22, 22, 22, 22, 22, 22, 21, 21, 21, 21, 21, 21, 21, 20, 20, 20, 19, 19, 19, 19, 19, 19, 19, 18, 18, 18, 17, 17, 17, 17

Since there are 36 scores (even), the median will be the average of the 18th and 19th scores:

18th score = 21
19th score = 20

Median = (21 + 20) / 2 = 20.5

### Mode

The mode is the score that appears most frequently:

- The most frequent scores are 21 and 19 (both appearing 7 times).

### Summary of Results:
- Total Frequency: 36
- Mean ACT Score: 20.33
- Median ACT Score: 20.5
- Mode ACT Score: 21 and 19 (bimodal)

Let me know if you need any further analysis or information!