Chapter 12, Problem 7CT

To determine

To find: the mean, median, mode and range of the diver weight with tanks.

Answer to Problem 7CT

Here mean is $109.6$ ,median is $109.5$ , range is $15$ and there is no mode.

Explanation of Solution

Given:

The weights of scuba divers without tanks are:

  $85,103,94,97,88,91,104,95$ .

The weight of a tank is $15\text{kg}$ .

Concept used:

Arithmetic mean:

Mean: $\stackrel{-}{x}=\frac{{\displaystyle \sum xi}}{N}$ .

Median $=\left\{\begin{array}{c}\frac{N}{2}\text{th term; }N\text{ is odd}\\ \frac{N}{2}\text{th term; }N\text{ is even}\end{array}\right\}$ .

Mode= the value in the data set that occurs most frequently.

Calculation:

According to given the weights of scuba divers without tanks are:

  $85,103,94,97,88,91,104,95$ .

The weight of a tank is $15\text{kg}$ .

Without tank:

Mean is the average of the data:

  $\stackrel{-}{x}=\frac{85+88+91+94+95+97+103+104}{8}$ .

  $\Rightarrow \frac{757}{8}\approx 94.6$ .

The mean $\stackrel{-}{x}=94.6$ .

Median is calculated by making the order in increasing order and then choose the middle value.

If the number of the data is even then there will have two middle value so, by taking the mean of two middle value get the median as:

The data in increasing order is:

  $85,88,91,94,95,97,103,104$ .

Total number of data is $8$ which is even so there will be two middle value which is $94,95$ by taking mean of two middle value:

  $\frac{94+95}{2}=94.5$ .

The median is $94.5$ .

Mode is the value that occurs maximum or most often.

Taking the increasing order of the data:

  $85,88,91,94,95,97,103,104$ .

Here there is no mode since, there is no number which is occurred maximum.

Range is the difference between largest and smallest value.

Taking the increasing order of the data:

  $85,88,91,94,95,97,103,104$ .

Here largest value is $104$ and smallest value is $85$ .

  $104-85=19$ .

The range here is $19$ .

With tanks

Tank weighs $15\text{kg}$ add $15$ to the mean, median and mode the range will still be the same.

Hence, mean is $109.6$ ,median is $109.5$ , range is $15$ and there is no mode.