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 representative of the 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 central tendency? 1950 1100 1050 1100 1250 1200 1100 1850 1200 1500 1100 1750. c. 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. d. the sample consists of the \best buy\ tvs, so it is a random sample and is likely to be representative of the population. if you decide to buy one of these tvs, what statistic is most relevant, other than the measures of central tendency? choose the best answer below. a. the lowest price is a relevant statistic for someone planning to buy one of the tvs. b. the price that occurs least frequently is a relevant statistic for someone planning to buy one of the tvs. c. the highest price is a relevant statistic for someone planning to buy one of the tvs. d. the difference between the lowest price and the highest price is a relevant statistic for someone planning to buy one of the tvs.

Explanation:

Step1: Calculate the mean

Sum of data values: $1950 + 1100+1050 + 1100+1250+1200+1100+1850+1200+1500+1100+1750=16250$
Number of data - points $n = 12$
Mean $\bar{x}=\frac{16250}{12}\approx1354.17$

Step2: Calculate the median

Arrange data in ascending order: $1050,1100,1100,1100,1100,1200,1200,1250,1500,1750,1850,1950$
Since $n = 12$ (even), median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values.
$\frac{12}{2}=6$ and $\frac{12}{2}+1 = 7$
Median $=\frac{1200 + 1200}{2}=1200$

Step3: Calculate the mode

The mode is the value that appears most frequently. Here, $1100$ appears $4$ times, so the mode is $1100$.

Step4: Calculate the mid - range

Mid - range $=\frac{\text{Minimum value}+\text{Maximum value}}{2}=\frac{1050 + 1950}{2}=1500$

Step5: Analyze representativeness

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 of all 60 - inch and larger TVs.

Step6: Find relevant statistic for buying

For someone planning to buy a TV, the lowest price is a relevant statistic as it gives an idea of the minimum cost.

Answer:

(a) Mean: $\approx1354.17$
(b) Median: $1200$
(c) Mode: $1100$
(d) Mid - range: $1500$
(e) The sample is not representative of the population. The relevant statistic for buying (other than measures of central tendency) is A. The lowest price is a relevant statistic for someone planning to buy one of the TVs.