12,14,15,04,9,9,7,7,7,2,5,7,9,12,13. Find mean mode and median of ... - Free Printable

Problem Analysis:

The task involves calculating the mean, mode, and median of a given dataset. The dataset is provided as follows:

$$
12, 14, 15, 04, 9, 9, 7, 7, 7, 2, 5, 7, 9, 12, 13
$$

#### Step 1: Calculate the Mean
The mean is the average of all the numbers in the dataset. It is calculated using the formula:

$$
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}
$$

- Step 1.1: Sum all the values in the dataset.
$$
12 + 14 + 15 + 4 + 9 + 9 + 7 + 7 + 7 + 2 + 5 + 7 + 9 + 12 + 13
$$

Let's add them step by step:
$$
12 + 14 = 26
$$
$$
26 + 15 = 41
$$
$$
41 + 4 = 45
$$
$$
45 + 9 = 54
$$
$$
54 + 9 = 63
$$
$$
63 + 7 = 70
$$
$$
70 + 7 = 77
$$
$$
77 + 7 = 84
$$
$$
84 + 2 = 86
$$
$$
86 + 5 = 91
$$
$$
91 + 7 = 98
$$
$$
98 + 9 = 107
$$
$$
107 + 12 = 119
$$
$$
119 + 13 = 132
$$

So, the sum of all values is:
$$
\text{Sum} = 132
$$

- Step 1.2: Count the number of values in the dataset.
There are 15 values in the dataset.

- Step 1.3: Calculate the mean.
$$
\text{Mean} = \frac{132}{15}
$$

Simplify the fraction:
$$
\text{Mean} = 8.8
$$

#### Step 2: Determine the Mode
The mode is the value that appears most frequently in the dataset.

- Step 2.1: List the frequency of each value:
$$
\begin{aligned}
&2: 1 \quad (appears once) \\
&4: 1 \quad (appears once) \\
&5: 1 \quad (appears once) \\
&7: 4 \quad (appears four times) \\
&9: 3 \quad (appears three times) \\
&12: 2 \quad (appears twice) \\
&13: 1 \quad (appears once) \\
&14: 1 \quad (appears once) \\
&15: 1 \quad (appears once)
\end{aligned}
$$

- Step 2.2: Identify the value with the highest frequency.
The value 7 appears 4 times, which is more frequent than any other value.

Therefore, the mode is:
$$
\text{Mode} = 7
$$

#### Step 3: Determine the Median
The median is the middle value when the dataset is arranged in ascending order. If the number of values is odd, the median is the middle value. If the number of values is even, the median is the average of the two middle values.

- Step 3.1: Arrange the dataset in ascending order:
$$
2, 4, 5, 7, 7, 7, 7, 9, 9, 9, 12, 12, 13, 14, 15
$$

- Step 3.2: Identify the middle value.
Since there are 15 values (an odd number), the median is the 8th value in the ordered list.

Counting to the 8th value:
$$
2, 4, 5, 7, 7, 7, 7, \mathbf{9}, 9, 9, 12, 12, 13, 14, 15
$$

The 8th value is:
$$
\text{Median} = 9
$$

Final Answers:

$$
\boxed{8.8, 7, 9}
$$