Question

an electronics store placed an ad in the newspaper showing flat - screen tvs for sale. the ad says \our flat - screen tvs average $700.\ the prices of the flat - screen tvs are $1199, $949, $1449, $979, $700, $1095, $1295, and $700.
a. find the mean, median, and mode of the prices.
the mean is $1045.75. (round to the nearest cent as needed.)
the median is $700. (round to the nearest cent as needed.)
b. which measure is the store using in its ad? why did they choose it?
c. which measure would a consumer want to see advertised? explain.

Explanation:

Step1: Identify the prices

The prices of the flat - screen TVs are: $1199, $949, $1449, $979, $700, $1095, $1295, $700. Let's first sort them in ascending order: $700, $700, $949, $979, $1095, $1199, $1295, $1449.

Step2: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n$ is the number of data points and $x_{i}$ are the data values.
$\sum_{i=1}^{8}x_{i}=700 + 700+949 + 979+1095+1199+1295+1449$
$=700\times2+949 + 979+1095+1199+1295+1449$
$=1400+949+979+1095+1199+1295+1449$
$=1400+(949 + 979)+(1095+1199)+(1295+1449)$
$=1400 + 1928+2294+2744$
$=1400+1928=3328$; $3328 + 2294=5622$; $5622+2744 = 8366$
$n = 8$
Mean $\bar{x}=\frac{8366}{8}=1045.75$

Step3: Calculate the median

For $n = 8$ (even number of data points), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th values.
$\frac{n}{2}=\frac{8}{2}=4$ and $\frac{n}{2}+1 = 5$
The 4th value is $979$ and the 5th value is $1095$
Median $=\frac{979 + 1095}{2}=\frac{2074}{2}=1037$ (Wait, there is a mistake in the original given median. Let's recalculate. Wait, maybe I misread the data. Let's check the original problem again. Wait, the user - provided data in the image: maybe the prices are $1199, $949, $1449, $979, $700, $1095, $1295, $700. Wait, when sorted: $700, $700, $949, $979, $1095, $1199, $1295, $1449. The 4th term is $979$, 5th term is $1095$. Median $=\frac{979 + 1095}{2}=\frac{2074}{2}=1037$. But the original says median is $700$, which is wrong. Maybe there is a mis - transcription. But according to the user's given a part, we will follow the steps as per the problem.

Step4: Calculate the mode

The mode is the value that appears most frequently. Here, $700$ appears twice, and all other values appear once. So the mode is $700$.

Step5: Analyze part b

The store used the mode ($700$) in its ad. Because the mode is the most frequently occurring price, and it is the lowest price among the measures (mean is $1045.75$, median we calculated as $1037$, mode is $700$). A lower price is more attractive to customers, so the store chose the mode to make the TV prices seem more affordable.

Step6: Analyze part c

A consumer would want to see the mean or the median. The mean ($1045.75$) and the median ($1037$) give a more accurate representation of the "average" price. The mode is the lowest price and is a bit misleading as it only represents the most frequent price, not the typical price. The mean takes into account all the prices, and the median is also a good measure of central tendency that is not affected by extreme values as much as the mean (but in this case, the highest price is $1449$ and the lowest is $700$). So a consumer would want to see the mean or the median to get a better idea of the typical price of the TVs.

Answer:

a. Mean: $\$1045.75$, Median: $\$1037$ (corrected), Mode: $\$700$
b. The store used the mode ($\$700$) in its ad. It chose the mode because it is the lowest price among the measures of central tendency, which is more likely to attract customers as it makes the TVs seem more affordable.
c. A consumer would want to see the mean or the median. The mean and median give a more accurate representation of the typical price of the TVs, while the mode ($\$700$) is misleading as it only reflects the most frequent price, not the overall average or typical price.