Q54. - Algebra 1

Question

Which of the following is a true statement.

A. The mode is the same as the median.

B. The median is the same as the mean.

C. The range is the same as the model.

D. The mode is the same as the mean.

Step-by-Step Solution

Answer

The mode is the same as the median. So, option (A) is true.

Step 1. Given information.

Stacy’s first five science test scores were 95, 86, 83, 95, and 99.

Step 2. Write the concept.

The mean of the data is the ratio of the sum of observations to the total number of observations.

For the median of the data, arrange the data in ascending or descending order.

If n is the number of variables in the data, then the median is given by the following formula.

Median $=\frac{n+1}{2}\text{th}$ variable; when n is odd.

And

Median $=\frac{1}{2}\left\{\frac{n}{2}\text{th\hspace{0.17em}\hspace{0.17em}variable\hspace{0.17em}}+\left(\frac{n}{2}+1\right)\text{th\hspace{0.17em}\hspace{0.17em}variable}\right\}$; when n is even.

The mode of the data is the observation that occurs most of the time.

The range of a data set is the difference between the largest value and the smallest value.

Step 3. Find the mean.

The mean of the data is:

$$\begin{gathered} \text{Mean}=\frac{83+86+95+95+99}{5} \\ =\frac{458}{5} \\ =91.6 \end{gathered}$$

Step 4. Find the mode.

In the data set, 95 occurs 2 times.

So,

The mode of the data is 95.

Step 5. Find the median.

The data set is written in ascending order:

83, 86, 95, 95, 99

Since, $n=5$ which is odd.

So,

$$\begin{gathered} \text{Median}=\frac{5+1}{2}\text{th\hspace{0.17em}\hspace{0.17em}variable} \\ =\frac{6}{2}\text{th\hspace{0.17em}\hspace{0.17em}variable} \\ =3\text{rd\hspace{0.17em}\hspace{0.17em}variable} \\ =95 \end{gathered}$$

Step 6. Find the range.

Since, the largest value = 99 and the smallest value = 83

 So,

Range $=99-83=16$

Step 7. Conclusion.

From above, conclude that the mode is the same as the median.