Chapter 11.3, Problem 1Q

To determine

To find the mean, median and mode of data set.

Answer to Problem 1Q

Mean $=3$

Median = $3.25$

Mode = $\frac{7}{2}$

Explanation of Solution

Given information: $\frac{7}{2},5,\frac{5}{2},3,\frac{7}{2},\frac{1}{2}$

Formula Used: Mean = $\frac{Sumofallobservations}{Totalobservations}$ , Median = $\frac{{\left(\frac{n}{2}\right)}^{th}+{\left(\frac{n}{2}+1\right)}^{th}}{2}term$ , Mode = Most repeated value.

Calculation:

  $\frac{7}{2},5,\frac{5}{2},3,\frac{7}{2},\frac{1}{2}$

Now, in Ascending Order

  $\frac{1}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2},5$

• Mean

Mean = $\frac{Sumofallobservations}{Totalobservations}$

So,

Mean = $\frac{\frac{1}{2}+\frac{5}{2}+3+\frac{7}{2}+\frac{7}{2}+5}{6}$

Now,

Mean = $\frac{36}{12}$

Hence,

Mean $=3$

• Median

Median = $\frac{{\left(\frac{n}{2}+1\right)}^{th}term+{\left(\frac{n}{2}\right)}^{th}term}{2}$

So,

Median = $\frac{{\left(\frac{6}{2}+1\right)}^{th}term+{\left(\frac{6}{2}\right)}^{th}term}{2}$

Now,

Median = $\frac{{\left(3\right)}^{rd}term+4^{th}term}{2}$

As, Median = $\frac{3+3.5}{2}$

Hence,

Median = $3.25$

• Mode

Mode = Most repeated value.

So,

  $\frac{7}{2}$ Is the most repeated value.

Mode = $\frac{7}{2}$

Mean best describes the central tendency of the data.