Question

for the following data set {1, 6, 2, 1, 5}, compute the mean, median, mode, range, and the distance (deviation) each value is from the mean

(type an integer or a decimal )

the median is 2
(type an integer or a decimal )

determine the mode(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the mode is 1
(use a comma to separate answers as needed. type an integer or a decimal )

b. there is no mode

the range is 5
(type an integer or a decimal )

subtract the mean from each value to find that value’s deviation from the mean.

the value 1 has a deviation from the mean of
the value 6 has a deviation from the mean of
the value 2 has a deviation from the mean of
the value 1 has a deviation from the mean of
the value 5 has a deviation from the mean of
(type integers or decimals )

Explanation:

Step1: Calculate the mean

First, find the sum of the data set \(\{1, 6, 2, 1, 5\}\). The sum is \(1 + 6 + 2 + 1 + 5 = 15\). There are 5 data points, so the mean \(\bar{x}=\frac{15}{5}=3\).

Step2: Find deviation for each value

• For value 1: Deviation is \(1 - 3 = -2\)
• For value 6: Deviation is \(6 - 3 = 3\)
• For value 2: Deviation is \(2 - 3 = -1\)
• For value 1: Deviation is \(1 - 3 = -2\) (same as the first 1)
• For value 5: Deviation is \(5 - 3 = 2\)

Answer:

The value 1 has a deviation from the mean of \(-2\)
The value 6 has a deviation from the mean of \(3\)
The value 2 has a deviation from the mean of \(-1\)
The value 1 has a deviation from the mean of \(-2\)
The value 5 has a deviation from the mean of \(2\)