Question

from unit 1, lesson 11 the dot - plot displays the number of marshmallows added to hot cocoa by several kids. marshmallows added to hot cocoa 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 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?

Explanation:

Step1: Calculate the mean of the data set from the dot - plot

First, find the sum of the data values and the number of data points. From the dot - plot, we have:
For value 3: 1 occurrence; for value 4: 1 occurrence; for value 5: 5 occurrences; for value 6: 1 occurrence; for value 7: 1 occurrence.
The sum of the data values is \(3\times1 + 4\times1+5\times5 + 6\times1+7\times1=3 + 4+25 + 6+7 = 45\).
The number of data points \(n=1 + 1+5 + 1+1=9\).
The mean \(\bar{x}=\frac{45}{9}=5\).

Step2: Calculate the absolute deviation for each data point

The absolute deviation of a data point \(x_i\) from the mean \(\bar{x}\) is \(|x_i-\bar{x}|\).
For \(x_1 = 3\), \(|3 - 5|=2\); for \(x_2 = 4\), \(|4 - 5|=1\); for \(x_3,x_4,x_5,x_6,x_7 = 5\), \(|5 - 5|=0\) (5 times); for \(x_8 = 6\), \(|6 - 5|=1\); for \(x_9 = 7\), \(|7 - 5|=2\).
The sum of the absolute deviations is \(2\times1+1\times1 + 0\times5+1\times1+2\times1=2 + 1+0 + 1+2 = 6\).

Step3: Calculate the Mean Absolute Deviation (MAD)

The MAD is the sum of the absolute deviations divided by the number of data points.
MAD\(=\frac{6}{9}=\frac{2}{3}\approx0.67\approx0.6\) (rounded to one - decimal place).

Answer:

A. 0.6 marshmallows