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?

1850 1950 1600 1950 1650 1000 1950 1400 1000 1700 1950 1150

a) Mean = $1,595.83

b) Median = $1,675

c) Mode = $1,950

d) Midrange = $1,475

e)

- No, the resulting statistics are not representative of the population of all TVs that are 60 inches and larger because it is given that the dataset provided is for the selling prices of TVs that are 60 inches or larger and rated as a "best buy" by a popular magazine, hence, this dataset is representative of the best type of TVs that are 60 inches and larger and not all TV sets.

- The statistic that is most relevant other than the measures of central tendency is the standard deviation, a measure of dispersion It shows the variation of the selling prices of different best TVs that are 60 inches and larger, especially their variations from the mean.

Step-by-step explanation:

The data set for selling prices of TVs that are 60 inches or larger and rated as a "best buy" by a popular magazine.

1850   1950   1600   1950   1650   1000   1950   1400   1000   1700   1950   1150

a) Mean

The mean is the sum of all the variables in the distribution divided by the number of variables.

Mean = (Σx)/N = (1850+1950+1600+1950+1650+1000+1950+1400+1000+1700+1950+1150)/12

= (19,150/12) = $1,595.83

b) Median

The median is the variable that falls at the middle of the distribution when all the variables are arranged in ascending or descending order.

Arranging this dataset

1000, 1000, 1150, 1400, 1600, 1650, 1700, 1850, 1950, 1950, 1950, 1950   

The numbers in the middle of this distribution include the sixth and seventh variables respectively, 1650 and 1700

Median = (1650+1700)/2 = $1,675

c) Mode

The mode is the variable with the highest frequency in the distribution. It is the variable that occurs the most in the distribution.

Evidently, the selling price with the highest frequency or the selling price that occurs the most in this distribution = $1950

d) Midrange

The midrange is given mathematically as

Midrange = [(Highest variable) + (lowest variable)] ÷ 2

Highest variable = 1950

Lowest variable = 1000

Midrange = (1950+1000)/2 = $1475

e)

- No, the resulting statistics are not representative of the population of all TVs that are 60 inches and larger because it is given that the dataset provided is for the selling prices of TVs that are 60 inches or larger and rated as a "best buy" by a popular magazine, hence, this dataset is representative of the best type of TVs that are 60 inches and larger and not all TV sets.

- The statistic that is most relevant other than the measures of central tendency is the standard deviation, a measure of dispersion It shows the variation of the selling prices of different best TVs that are 60 inches and larger, especially their variations from the mean.

Hope this Helps!!!