Answer :

GinnyAnswer
Let’s analyze the set of data [tex]\( \{8, 8, 9, 10, 10\} \)[/tex] to determine its mean, median, and mode.

### Mean
The mean is the average of the data set. To find the mean, we sum all the numbers and divide by the number of observations.

[tex]\[ \text{Mean} = \frac{\text{Sum of the data values}}{\text{Number of data values}} \][/tex]

Sum of the data values:
[tex]\[ 8 + 8 + 9 + 10 + 10 = 45 \][/tex]

Number of data values:
[tex]\[ 5 \][/tex]

So, the mean is:
[tex]\[ \text{Mean} = \frac{45}{5} = 9 \][/tex]

### Median
The median is the middle value when the data set is ordered from least to greatest.

Here, the ordered data set is:
[tex]\[ 8, 8, 9, 10, 10 \][/tex]

Since there are 5 data points (an odd number), the median is the third value in the ordered list:
[tex]\[ \text{Median} = 9 \][/tex]

### Mode
The mode is the value that appears most frequently in the data set.

In this data set:
- 8 appears twice,
- 9 appears once,
- 10 appears twice.

Both 8 and 10 appear most frequently, each occurring twice.

Thus, the mode is:
[tex]\[ \text{Mode} = 8 \text{ and } 10 \][/tex]

However, if we are looking for a single mode in case of a requirement for unimodal data, we may state that the data set is bimodal because there are two values with the same highest frequency.

Given the mean, median, and mode calculated, the true statements for this data set are:

1. The mean is 9.
2. The median is 9.
3. The mode includes both 8 and 10, indicating it is bimodal.

So, all our calculations and interpretations align with these statements.

Other Questions