Question

Five students scored 80 on a test, five students scored 85, and five students scored 90.

Complete each statement below by inserting the correct number.

a. The mean is equal to .

b. The median is equal to .

c. The range is equal to .

d. The mode is equal to .

Answer 1

Let's analyze the scores of the 15 students:

- 5 students scored 80
- 5 students scored 85
- 5 students scored 90

We will calculate each statistical measure step by step.

### a. Mean
To calculate the mean, we need to find the sum of all scores and then divide by the number of students.

\[
\text{Total score} = (5 \times 80) + (5 \times 85) + (5 \times 90)
\]
\[
= 400 + 425 + 450 = 1275
\]

Now we divide by the number of students:

\[
\text{Mean} = \frac{\text{Total score}}{\text{Number of students}} = \frac{1275}{15} = 85
\]

**The mean is equal to 85.**

### b. Median
To find the median, we need to arrange the scores in order. The scores are:

- 80, 80, 80, 80, 80
- 85, 85, 85, 85, 85
- 90, 90, 90, 90, 90

Since there are 15 scores, the median will be the score of the 8th student (the middle score):

- The first 5 scores are 80
- The next 5 scores are 85
- The 8th score is 85

**The median is equal to 85.**

### c. Range
The range is calculated by taking the difference between the highest and lowest scores.

\[
\text{Range} = \text{Highest score} - \text{Lowest score} = 90 - 80 = 10
\]

**The range is equal to 10.**

### d. Mode
The mode is the score that occurs most frequently. Here:

- 80 appears 5 times
- 85 appears 5 times
- 90 appears 5 times

Since all three scores appear with the same highest frequency, we have:

**The mode is equal to 80, 85, 90 (or it can be stated as "no single mode").**

To summarize:

a. The mean is equal to **85**.

b. The median is equal to **85**.

c. The range is equal to **10**.

d. The mode is equal to **80, 85, 90** (or "no single mode").