Chapter 3.1, Problem 33E

(a)

To determine

To calculate the mean number of shots.

Answer to Problem 33E

The mean number of shots per camera is $201.3$

Explanation of Solution

Given information:

Camera	Number of shots
Panasonic lumix $\text{DMC-3D1}$	$200$
Canon $\text{ELPH 115}\text{IS}$	$200$
Nikon Coolpix $\text{P330}$	$200$
Fujifilm FinePix $\text{JX500}$	$170$
Sony Cyber shot $\text{DSC}-\text{TX200V}$	$220$
$\text{GE}\text{E1410SW}$	$150$
Fujifilm FinePix $\text{JX}580$	$170$
Panasonic Lumix $\text{DMC}-\text{FH}8$	$260$
Nikon Coolpix $\text{S}01$	$190$
Sony cyber shot $\text{DSC}-\text{W}650$	$220$
Sony Cyber shot $\text{DSC}-\text{W690}$	$220$
Canon Power shot $\text{A2300}$	$210$
Panasonic Lumix $\text{DMC}-\text{ESZ}1$	$250$
Nikon Coolpix $\$3300$	$210$
Fujifilm FinePix $\text{JZ}250$	$180$
Fujifilm FinePix $\text{T}400$	$160$
Nikon Coolpix $\$3500$	$220$
Sony Cyber shot $\text{DSC}-\text{W710}$	$220$
Canon Power shot $A4000\text{ IS}$	$175$

Formula used:

$\overline{x}=\frac{{\displaystyle \sum x}}{n}$

Calculation:

Compute the mean number of shots by using the formula is given below.

$\begin{array}{c}\overline{x}=\frac{{\displaystyle \sum x}}{n}\\ =\frac{\left(\begin{array}{l}200+200+200+170+220+150+170+260+190+220\\ +220+210+250+210+180+160+220+220+175\end{array}\right)}{19}\\ =\frac{3,825}{19}\\ =201.3\end{array}$

Thus, the mean number of shots per camera is $201.3$

(b)

To determine

To calculate the median number of shots.

Answer to Problem 33E

The median number of shots is $200$

Explanation of Solution

Given information:

First, arrange the data in ascending order. $150,160,170,170,175,180,190,200,200,200,210,210,220,220,220,220,220,250,260$

Calculation:

Compute the median number of shots.

Here, there are $19$ observations in the data. That is, the sample size $n\left(=19\right)$ is odd.

Thus, the median is the middle value and lies at the ${\left(\frac{n+1}{2}\right)}^{th}$ position, when the data are in ascending order,

First, arrange the data in ascending order. $150,160,170,170,175,180,190,200,200,200,210,210,220,220,220,220,220,250,260$

Hence, the median lies at the ${\left(\frac{19+1}{2}\right)}^{th}$ position. That is, the median value lies at the 10^{t h} position.

Therefore, the median number of shots is $200$.

(c)

To determine

To calculate the mode of the data.

Answer to Problem 33E

The value of mode is $220$

Explanation of Solution

Calculation:

Compute the mode or modes.

Here, the value $170$ is repeated two times, the value $200$ is repeated three times, the value $210$ is repeated two times and the value $220$ is repeated five times. Hence, the shots $\text{170, 200, 210, and 220}$ are possible modes. But, the greatest frequency for $\text{220 shot is 5}$.

Hence, the value of mode is $220$

(d)

To determine

To explain the shape of the distribution of the data.

Answer to Problem 33E

The given data is approximately symmetric because the value of mean is approximately close to the value of median.

Explanation of Solution

Given information:

Mean = $201.3$ and median = $200$

A data set is said to be symmetric when mean and median are approximately equal to each other. When mean is greater than median then data is positively skewed and if median is greater than mean than data set is left skewed.

The given data is approximately symmetric because the value of mean is approximately close to the value of median.