Chapter 13, Problem 12SGR

To determine

The best measures of central tendency for the length of movies played at theatrefor $138,117,158,135,120\text{min}$ is to be estimated.

Answer to Problem 12SGR

The best measures of central tendency for the length of movies played at theatrefor $138,117,158,135,120\text{min}$ is median.

Explanation of Solution

Given:

Length of movies played at theatre $138,117,158,135,120\text{min}$

Concept Used:

Mean is given by the following expression:

  $X=\frac{{\displaystyle \sum }}{n}$

Where,

Sum of data point: ${\displaystyle \sum }$

Number of data point: $n$

Median:

To find the median of the data points, the arrangement of numbers from the least to greatest has to be used.

For the even number of system, the mean of middle two numbers has to calculated which nothing but a median of even data

In case of odd numbers system take middle one number which is the median of system.

Mode:

The number which occurs most of times in the system is known as the mode.

A typical value of data set or centre point which represents the statistical summary is known as a measure of central tendency.

Calculation:

Mean of the given the length of movies played at theatreis calculated as:

  $\begin{array}{l}X=\frac{{\displaystyle \sum }}{n}\\ X=\frac{{\displaystyle \sum \left(138+117+158+145+135+120\right)}}{6}\\ X=\frac{813}{6}\\ X=135.5\end{array}$

Median of length of movies played at theatreis calculated as:

Take length of movies played at theatrefrom the least to greatest:

  $117,120,135,138,158$

Here is an odd number of system, so take the middle one numberwhich nothing but a median of odd data.

So, the median of the odd number system is $135$ .

Modeof length of movies played at theatreis calculated as:

Here, no number is repeated that means there is no mode for the given length of movies played at theatre.

Now the best measure of central tendency is represented by the median because the data has extreme value but doesn’t contain much gap in the middle numbers.

Conclusion:

Hence,the results of giveninches of rain last week are as:

Mean: $135.5$

Median: $135$

No mode.