Pamela called nine repair shops for quotes for auto repairs. The prices are $139, $150, $345, $99, $167, $155, $140, $200, and $160. She thinks there is a chance that there is an outlier and the data may be biased. Which measure of central tendency should she choose and what value would best represent the central tendency?

For her to check whether there is an outlier in the data, she needs to find the mean of the set of data. An outlier is a value in a set of a data that varies considerably from other data in a dataset. It may be larger or smaller than other set of datas. An outlier can affect the decision of a set of data to be analysed if nor taken care of.

From the data, the possible outliers are $99 and $345

Mean of the data = sum of all the prices/sample size

xbar = \sum Xi / N

Xi are individual datas

\sum Xi = $139+$150+$345+$99+$167+$155+$140+$200+$160

\sumXi = $1555

Sample size = 9

Mean = $1555/9

Mean = $172.78

Hence the value that would best represent the central tendency is $177.78

MrRoyal MrRoyal · Answer 2 · 2021-12-23T12:42:42+01:00

The best measure of central tendency to use is the median, and the value that best represents the measure of central tendency is 155

The prices are given as:

$139, $150, $345, $99, $167, $155, $140, $200, and $160

The mean of a dataset can be affected by an outlier; however, the median of a dataset cannot be affected by outliers.

So, the best measure of central tendency to use is the median.

To calculate the median, we start by arranging the dataset in ascending order

$99, $139, $140, $150, $155, $160, $167, $200, $345

Then we select the middle element as the median.

Hence, the median price is $155