To find the mean, median, and mode of the given data set, we'll consider each statistical measure one by one.
### Step 1: Mean
The mean (or average) of a data set is the sum of all the values divided by the number of values. The data set is:
[tex]\[ \frac{3}{4}, \frac{2}{5}, \frac{1}{10}, \frac{3}{4}, \frac{1}{4} \][/tex]
The sum of these values is:
[tex]\[ \frac{3}{4} + \frac{2}{5} + \frac{1}{10} + \frac{3}{4} + \frac{1}{4} \][/tex]
Dividing this sum by the number of values (which is 5) gives us the mean.
### Step 2: Median
The median is the middle value of a data set when it is ordered from smallest to largest. If the data set has an odd number of values, the median is the middle value. If it has an even number of values, the median is the average of the two middle values.
First, order the data set:
[tex]\[ \frac{1}{10}, \frac{1}{4}, \frac{2}{5}, \frac{3}{4}, \frac{3}{4} \][/tex]
Since there are 5 values (an odd number), the median is the third value:
[tex]\[ \frac{2}{5} \][/tex]
### Step 3: Mode
The mode is the value that appears most frequently in the data set. Here, we see that:
[tex]\[ \frac{3}{4} \][/tex]
appears twice, whereas the other values appear only once. Hence, the mode is:
[tex]\[ \frac{3}{4} \][/tex]
### Answers
Based on these calculations:
- The mean is [tex]\( 0.45 \)[/tex] or [tex]\( \frac{9}{20} \)[/tex].
- The median is [tex]\( 0.4 \)[/tex] or [tex]\( \frac{2}{5} \)[/tex].
- The mode is [tex]\( 0.75 \)[/tex] or [tex]\( \frac{3}{4} \)[/tex].
Therefore, the best answer from the choices provided is:
c. mean: [tex]\( 9 / 20 \)[/tex], median: [tex]\( 2 / 5 \)[/tex], mode: [tex]\( 3 / 4 \)[/tex]
