Question

item 6
a data set of ten numbers has a range of 150 and a mean of 62. when the largest number is removed from the data set, the mean dropped to 34. what is true about the largest number?
a
it had a value of 150.
b
it was an outlier.
c
it was within 10 of the original mean.
d
it had a value of 62.

Explanation:

Step1: Calculate the sum of the original data set

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Given \(n = 10\) and \(\bar{x}=62\), the sum of the original data set \(S_{10}=n\times\bar{x}=10\times62 = 620\).

Step2: Calculate the sum of the data set after removing the largest number

After removing the largest number, \(n = 9\) and \(\bar{x}=34\). The sum of the new data set \(S_{9}=n\times\bar{x}=9\times34=306\).

Step3: Find the value of the largest number

The value of the largest number \(x = S_{10}-S_{9}\). Substitute the values: \(x=620 - 306=314\). Since the range of the original data set is \(150\) (range \(R=\text{Max}-\text{Min}\)), if the largest number \(x = 314\), it is an outlier (a value that is much larger than the other values in the data - set).

Answer:

B. It was an outlier.