1. Jack wants to buy a pair of name-brand headphones on a popular auction website. He enters the brand, make, and model number and searches the site

for what is available. He notices that some headphones are being offered as

"buy now" with a fixed price and others are up for bid in auctions. Below is a

list of all prices at the time he did his search.

$75 $95 $180 $136 $89 $75 $110 $180 $100 $136 $180

$95 $180 $136 $75

$100 $110 $180 $180 $136 $75 $90

a. Construct a frequency distribution for the data.

b. Use the frequency distribution to determine the mean. Round your answer

to the nearest cent.

c. Use the frequency distribution to determine the median and the mode.

The mean of the frequency distribution is $125.136, the median of the frequency distribution is $110, and the mode of the frequency distribution is $180.

Given :

a) The frequency distribution is given below:

Prices              Frequency       Cumulative Frequency

85                           4                                 4

89                            1                                 5

90                            1                                  6

95                            2                                  8

100                           2                                 10

110                            2                                  12

136                            4                                 16

180                            6                                 22

b) The mean is calculated as:

Simplify the above expression.

Mean = $125.136

c) The median of the frequency distribution is calculated as:

So, the median is $110.

The mode of the frequency distribution is $180.

For more information, refer to the link given below:

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Mean = 125.136

Median = 110

Mode = 180

Step-by-step explanation:

Given the data:

75 95 180 136 89 75 110 180 100 136 180 95 180 136 75 100 110 180 180 136 75 90

Frequency distribution:

Value(X) ___freq (F) cumm frequency

85 4 4

89 1 5

90 1 6

95 2 8

100 2 10

110 2 12

136 4 16

180 622

2) Using the frequency distribution :

Mean = Σfx / Σf

[(85*4) + (89*1) + (90*1) + (95*2) + (100*2) + (110*2) + (136*4) + (180*6)]/ 10

= 2753 / 22

= $125.136

Median of grouped data :

Frequency + 1 / 2 = 23/2 = 11.5 th term

The median value = $110

Mode of the data:

Most frequently occurring = 180 (frequency of 6)

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