Question

Find the mean, median, and mode for each set of data.

{52, 53, 53, 53, 55, 55, 57}

Short answer

The mean of the given data is 54, the median of the given data is 53, and the mode of the given data is also 53.

Step-by-step solution

Step 1. Write the formulae used.

• The mean of a data is: $\text{Mean}=\frac{\text{sumofallthenumbersindata}}{\text{Totalnumberofnumbersindata}}$
  
• The median of a data is calculated by arranging the numbers in data in ascending order then if:

1. The numbers in the data are odd, then the median is the middle term.
2. The numbers in data are even, then the median is the average of the middle term.

• The mode of data is the most repeated number of the data.

Step 2. Write the given information.

Numbers in data are(in ascending order): 52, 53, 53, 53, 55, 55, 57, i.e. there are 7 numbers in data.

Step 3. DESCRIPTION OF STEP.

Use the formulae mentioned to find mean, median and mode.

$$\begin{gathered} \text{Mean}=\frac{52+53+53+53+55+55+57}{\text{7}} \\ =\frac{378}{7} \\ =54 \end{gathered}$$

Since there are 7 numbers(odd) in data so the median is the middle term that is the 4th number, which is 53.

Thus, the median is 53.

And it can be noticed that 53 is repeated thrice and most of the time, i.e. mode of the data is 53.

Thus, the mean of the given data is 54, the median of the given data is 53, and the mode of the given data is also 53.