Question

find the (a) mean, (b) median, (c) mode, and (d) mid - range 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 a representation 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? 1400 1500 1850 1500 1100 1300 1500 1250 1300 1550 1500 1750
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.
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 highest price is a relevant statistic for someone planning to buy one of the tvs.
c. the difference between the lowest price and the highest price is a relevant statistic for someone planning to buy one of the tvs.
d. the price that occurs least frequently is a relevant statistic for someone planning to buy one of the tvs.

Explanation:

Step1: Calculate the mean

To find the mean $\bar{x}$, sum all the data values and divide by the number of data - points $n$. The data values are $1400, 1500, 1850, 1500, 1100, 1300, 1500, 1250, 1300, 1550, 1500, 1750$. The sum $\sum x=1400 + 1500+1850+1500+1100+1300+1500+1250+1300+1550+1500+1750 = 17500$. There are $n = 12$ data - points. So, $\bar{x}=\frac{\sum x}{n}=\frac{17500}{12}\approx1458.33$.

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 values. $\frac{n}{2}=6$ and $\frac{n}{2}+1 = 7$. The 6th value is $1500$ and the 7th value is $1500$. So, the median $M=\frac{1500 + 1500}{2}=1500$.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data - set. The value $1500$ appears $5$ times, more frequently than any other value. So, the mode $Mo = 1500$.

Step4: Calculate the mid - range

The mid - range is calculated as $\text{Mid - range}=\frac{\text{Minimum value}+\text{Maximum value}}{2}$. The minimum value is $1100$ and the maximum value is $1850$. So, $\text{Mid - range}=\frac{1100 + 1850}{2}=\frac{2950}{2}=1475$.

Step5: Answer part (e) first sub - question

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

Step6: Answer part (e) second sub - question

For someone planning to buy one of these TVs, the lowest price is a relevant statistic as it gives the least amount of money they might have to spend. The answer is A.

Answer:

(a) Mean: $\approx1458.33$
(b) Median: $1500$
(c) Mode: $1500$
(d) Mid - range: $1475$
(e) First sub - question: 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.
Second sub - question: A. The lowest price is a relevant statistic for someone planning to buy one of the TVs.