Question

find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given questions. listed below are selling prices (dollars) of tvs that are 60 inches or larger and rated as a \best buy\ by a popular magazine. are the resulting statistics population of all tvs that are 60 inches and larger? if you decide to buy one of these tvs, what statistic is most relevant, other than the measures of c 1400 1500 1850 1500 1100 1300 1500 1250 1300 1550 1500 1750 (type an integer or a decimal. do not round. use a comma to separate answers as needed.) b. there is no mode. d. find the midrange. the midrange is $ 1475.0 (type an integer or a decimal rounded to one decimal place as needed.) e. are the resulting statistics representative of the population of all tvs that are 60 inches and larger? choose the best answer below a. since the sample is random and the sample size is greater than 10, the sample should not be considered to be representative of the population. b. the sample consists of the \best buy\ tvs, so it is not a random sample and is not likely to be representative of the population. c. the sample consists of the \best buy\ tvs, so it is a random sample and is likely to be representative of the population. d. since the sample is random and the sample size is greater than 10, the sample can be considered to be representative of the population.

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data - points and $n$ is the number of data - points.
$n = 12$, and $\sum_{i=1}^{12}x_{i}=1400 + 1500+1850+1500+1100+1300+1500+1250+1300+1550+1500+1750 = 17500$.
So, $\bar{x}=\frac{17500}{12}\approx1458.33$.

Step2: Calculate the median

First, order the data: $1100,1250,1300,1300,1400,1500,1500,1500,1500,1550,1750,1850$.
Since $n = 12$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data - points.
The $\frac{n}{2}=6$th and $\frac{n}{2}+1 = 7$th ordered data - points are $1500$ and $1500$.
So, the median $=\frac{1500 + 1500}{2}=1500$.

Step3: Calculate the mode

The mode is the data - point that appears most frequently.
The number $1500$ appears $4$ times, more frequently than any other number. So, the mode is $1500$.

Step4: Analyze representativeness of the sample

The sample consists of "best - buy" TVs, so it is not a random sample of all 60 - inch or larger TVs. It is not likely to be representative of the population.

Answer:

a. $1458.33$
b. $1500$
c. $1500$
d. $1475.0$
e. B. The sample consists of the "best buy" TVs, so it is not a random sample and is not likely to be representative of the population.