Question

Bids were placed in a silent auction for a sword reputed to have been used at the Battle of Hastings, worth a reported $20,000. The respective bids (inthousands of dollars) placed by the 7 bidders were as follows.14, 15, 14, 14, 13, 25, 28Send data to calculator(a) What is the median of this data set? If your answer is notan integer, round your answer to one decimal place.(b) What is the mean of this data set? If your answer is not aninteger, round your answer to one decimal place.(c) How many modes does the data set have, and what aretheir values? Indicate the number of modes by clicking in theappropriate circle, and then indicate the value(s) of themode(s), it applicable.B10zero modesone mode:two modes:0and

Answer 1

Given: the data set below

`14,15,14,14,13,25,28(000-dollars)`

To Determine: The median, the mean, and the number of modes

Solution

To get the median, let arrange in ascending order as shown below

`13,14,14,14,15,25,28`

The median position is

`\begin{gathered} (N+1)/(2)th-position \\ N=7 \\ (7+1)/(2)th-position \\ (8)/(2)th-position \\ 4th-position \end{gathered}`

The median is in the 4th position position.

Hence the median is $14 thousands of dollars

(b) The mean can be calculated using the formula below

`\begin{gathered} mean=(\Sigma x)/(n) \\ mean=(13+14+14+14+15+25+28)/(7) \\ mean=(123)/(7) \\ mean=17.57142 \\ mean\approx17.6 \end{gathered}`

Hence, the mean is 17.6 thousands of dollars

(c) The mode is the number that appeared the most in the data. From the given data set, the number that appeared the most is 14

Hence, the data set has one mode, and the value of the mode is 14 thousands of dollars