Question

5 from unit 1, lesson 11
the dot plot displays the number of marshmallows added to hot cocoa by several kids.
what is the mean absolute deviation (mad) of the data represented in the dot plot?
a 0.6 marshmallows
b 3 marshmallows
c 4 marshmallows
d 5 marshmallows
6 from unit 1, lesson 12
here is a data set:
5 10 10 10 15 100
a. after studying the data, the researcher realized that the value 100 was meant to be recorded as 15. what happens to the mean and standard deviation of the data set when the 100 is changed to a 15?

b. for the original data set, with the 100, would the median or the mean be a better choice of measure for the center?
explain your reasoning.

Explanation:

Step1: <Find the mean of the data>

First, count the number of data points. There is \(1\) dot at \(3\), \(1\) dot at \(4\), \(6\) dots at \(5\), \(1\) dot at \(6\), \(1\) dot at \(7\). The total number of data points \(n=1 + 1+6 + 1+1=10\).
The data set is \(3,4,5,5,5,5,5,5,6,7\).
The mean \(\bar{x}=\frac{3 + 4+5\times6+6 + 7}{10}=\frac{3+4 + 30+6+7}{10}=\frac{50}{10}=5\).

Step2: <Calculate the absolute deviations>

For \(x = 3\): \(|3 - 5|=2\)
For \(x = 4\): \(|4 - 5|=1\)
For \(x = 5\) (6 times): \(|5 - 5|=0\) (6 times)
For \(x = 6\): \(|6 - 5|=1\)
For \(x = 7\): \(|7 - 5|=2\)
The sum of absolute deviations is \(2+1+0\times6 + 1+2=6\).

Step3: <Compute the MAD>

The Mean Absolute Deviation \(MAD=\frac{\sum_{i = 1}^{n}|x_{i}-\bar{x}|}{n}=\frac{6}{10}=0.6\).

Answer:

A. 0.6 marshmallows