Chapter 13, Problem 12STP

a.

To determine

The mean, median and mode of the given set of data.

Answer to Problem 12STP

Inches of rain last week $1.5,2,2.5,2,1.5,2.5,3$ has:

Mean: $12$

Median: $12$

No mode.

Explanation of Solution

Given:

Scores of Antoine: $13,15,9,10,14,11$

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.

Calculation:

Mean of the given scores of Antoineis calculated as:

  $\begin{array}{l}X=\frac{{\displaystyle \sum }}{n}\\ X=\frac{{\displaystyle \sum \left(13+15+9+10+14+11\right)}}{6}\\ X=\frac{72}{6}\\ X=12\end{array}$

Median of scores of Antoine is calculated as:

Take the scores of Antoine from the least to greatest:

  $9,10,11,13,14,15$

Here is even number of system, so take the mean of two middle numbers which nothing but a median of even data:

  $\begin{array}{l}X=\frac{11+13}{2}\\ X=12\end{array}$

So, the median of the even number system is $12$

Mode of scores of Antoine is calculated as:

Here, $9,10,11,13,14,15$ no number is repeated that means there is no mode for the given scores of Antoine.

Conclusion:

Hence, the results are as:

Mean: $12$

Median: $12$

No mode

b.

To determine

The measure of central tendency is to be explained which best describes the Antoine’s score production.

Answer to Problem 12STP

Best measure for the central tendency of the scores of Antoine production system is not present as the value of mean and median are same.

Explanation of Solution

Given:

Scores of Antoine: $13,15,9,10,14,11$

Concept Used:

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

For the given scores of Antoine production system, the values are calculated as:

Mean: $12$

Median: $12$

No mode is present because there is no repeating number in the given score list.

Now, in the given system of score there is same value for the mean and median. Due to one can-not compare these two values to find out the best measure for the central tendency.

Hence there is no best measure for the central tendency of the scores of Antoine production system.

Conclusion:

So, there is no best measure for the central tendency of the scores of Antoine production system.