Question

1. the dot - plot displays the number of marshmallows added by kids. what is the 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 11.)

Explanation:

Step1: Recall the formula for MAD

MAD (Mean - Absolute - Deviation) is the average of the absolute deviations from the mean. First, find the mean of the data set. Assume the data points from the dot - plot are: 3 (1 time), 4 (1 time), 5 (5 times), 6 (1 time). The data set is {3, 4, 5, 5, 5, 5, 5, 6}. The sum of the data points is \(3 + 4+5\times5 + 6=3 + 4+25 + 6=38\). There are \(1 + 1+5 + 1=8\) data points. The mean \(\bar{x}=\frac{38}{8}=4.75\).

Step2: Calculate the absolute deviations

For \(x_1 = 3\), the absolute deviation is \(|3 - 4.75|=1.75\). For \(x_2 = 4\), the absolute deviation is \(|4 - 4.75| = 0.75\). For \(x_3=x_4=x_5=x_6=x_7 = 5\), the absolute deviation is \(|5 - 4.75|=0.25\). For \(x_8 = 6\), the absolute deviation is \(|6 - 4.75| = 1.25\).

Step3: Calculate the sum of absolute deviations

The sum of absolute deviations is \(1.75+0.75+0.25\times5 + 1.25=1.75+0.75 + 1.25+1.25=5\).

Step4: Calculate the MAD

The MAD is \(\frac{5}{8}=0.625\approx0.6\).

Answer:

A. 0.6 marshmallows