To find the mean, median, and mode of the given data set, we need to follow a few steps for each measure.
1. Convert the fractions to decimal form:
- [tex]\( \frac{3}{4} = 0.75 \)[/tex]
- [tex]\( \frac{2}{5} = 0.4 \)[/tex]
- [tex]\( \frac{1}{10} = 0.1 \)[/tex]
- [tex]\( \frac{3}{4} = 0.75 \)[/tex] (again)
- [tex]\( \frac{1}{4} = 0.25 \)[/tex]
So, the data set in decimal form is: [tex]\[ 0.75, 0.4, 0.1, 0.75, 0.25 \][/tex]
2. Calculate the mean:
The mean (or average) is the sum of the values divided by the number of values.
[tex]\[
\text{Mean} = \frac{0.75 + 0.4 + 0.1 + 0.75 + 0.25}{5} = \frac{2.25}{5} = 0.45
\][/tex]
3. Find the median:
The median is the middle value when the data set is ordered from smallest to largest.
Ordering the data:
[tex]\[ 0.1, 0.25, 0.4, 0.75, 0.75 \][/tex]
The middle value (third value) is 0.4.
[tex]\[
\text{Median} = 0.4
\][/tex]
4. Identify the mode:
The mode is the value that appears most frequently.
In the data set [tex]\( 0.75, 0.4, 0.1, 0.75, 0.25 \)[/tex], 0.75 appears twice, which is more frequently than any other data point.
[tex]\[
\text{Mode} = 0.75
\][/tex]
Based on these calculations, the correct values are:
- Mean: 0.45
- Median: 0.4
- Mode: 0.75
Given the provided choices:
a. mean: [tex]\( \frac{1}{10} \)[/tex], median: [tex]\( \frac{1}{10} \)[/tex], mode: [tex]\( \frac{3}{4} \)[/tex]
b. mean: [tex]\( \frac{9}{20} \)[/tex], median: [tex]\( \frac{1}{10} \)[/tex], mode: [tex]\( \frac{3}{4} \)[/tex]
c. mean: [tex]\( \frac{9}{20} \)[/tex], median: [tex]\( \frac{2}{5} \)[/tex], mode: [tex]\( \frac{3}{4} \)[/tex]
d. mean: [tex]\( \frac{2}{5} \)[/tex], median: [tex]\( \frac{4}{9} \)[/tex], mode: [tex]\( \frac{3}{4} \)[/tex]
Evaluating each:
- [tex]\( \frac{9}{20} \)[/tex] is equivalent to 0.45 (mean)
- [tex]\( \frac{2}{5} \)[/tex] is equivalent to 0.4 (median)
- [tex]\( \frac{3}{4} \)[/tex] is equivalent to 0.75 (mode)
Therefore, the best answer is:
c. mean: [tex]\( \frac{9}{20} \)[/tex], median: [tex]\( \frac{2}{5} \)[/tex], mode: [tex]\( \frac{3}{4} \)[/tex]
