Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute themean, median, and mode.

1. Break Down the Problem

We need to find the mean, median, and mode of the given data values:
53, 55, 70, 58, 64, 57, 53, 69, 57, 68, 53.

2. Relevant Concepts

• Mean: The average of all data points, calculated as the sum of the values divided by the number of values.
• Median: The middle value when the data points are arranged in ascending order.
• Mode: The value that appears most frequently in the data set.

3. Analysis and Detail

Step 1: Calculate the Mean
$\text{Mean} = \frac{\sum \text{data values}}{N}$ Where $N$ is the number of data values.

• Total sum of values:
  $53 + 55 + 70 + 58 + 64 + 57 + 53 + 69 + 57 + 68 + 53 = 675$

• Number of data values:
  $N = 11$

• Mean calculation:
  $\text{Mean} = \frac{675}{11} \approx 61.36$

Step 2: Calculate the Median
First, we arrange the values in ascending order:
$53, 53, 53, 55, 57, 57, 58, 64, 68, 69, 70$

Since there are 11 values (odd number), the median is the middle value, which is the 6th value.
Median value:
$57$

Step 3: Calculate the Mode
The mode is the number that appears most frequently in the data set.
From the ordered values:

• 53 appears 3 times,
• 55 appears 1 time,
• 57 appears 2 times,
• 58 appears 1 time,
• 64 appears 1 time,
• 68 appears 1 time,
• 69 appears 1 time,
• 70 appears 1 time.

Since 53 appears the most frequently, the mode is:
Mode value:
$53$

4. Verify and Summarize

• Mean = $61.36$
• Median = $57$
• Mode = $53$

Final Answer

• Mean: $61.36$
• Median: $57$
• Mode: $53$