Question

lesson 11 practice problems
1 in science class, clare and lin estimate the mass of eight different objects that actually weigh 2,000 grams each. some summary statistics
clare

• mean: 2,000 grams
• mad: 275 grams
• median: 2,000 grams
• iqr: 500 grams

lin

• mean: 2,000 grams
• mad: 225 grams
• median: 1,950 grams
• iqr: 350 grams

which student was better at estimating the mass of the objects? explain your reasoning.
2 a reporter counts the number of times a politician talks about jobs in campaign speeches. what is the mad of the data represented in the dot - plot?
number of mentions of \jobs\
a 1.1 mentions
b 2 mentions
c 2.5 mentions
d 5.5 mentions

Explanation:

Step1: Understand the concept of MAD

MAD (Mean - Absolute - Deviation) measures the average distance between each data point and the mean. A lower MAD indicates that the data points are closer to the mean, meaning more consistent and accurate estimates.

Step2: Compare the MADs of Clare and Lin

Clare has a MAD of 275 grams and Lin has a MAD of 225 grams. Since 225 < 275, Lin's estimates are on average closer to the actual mass of 2000 grams.

for sub - question 2:

Step1: Calculate the mean

Count the number of data points. There are 1 + 1+ 3+ 3+ 1+ 1 = 10 data points. The sum of the data points is \(3\times1 + 4\times1+5\times3 + 6\times3+7\times1+8\times1=3 + 4+15 + 18+7+8 = 55\). The mean \(\bar{x}=\frac{55}{10}=5.5\).

Step2: Calculate the absolute - deviations

For \(x = 3\), the absolute - deviation is \(|3 - 5.5|=2.5\); for \(x = 4\), \(|4 - 5.5| = 1.5\); for \(x = 5\), \(|5 - 5.5|=0.5\); for \(x = 6\), \(|6 - 5.5| = 0.5\); for \(x = 7\), \(|7 - 5.5|=1.5\); for \(x = 8\), \(|8 - 5.5| = 2.5\).

Step3: Calculate the MAD

Multiply each absolute - deviation by the frequency of the data point: \((2.5\times1+1.5\times1 + 0.5\times3+0.5\times3+1.5\times1+2.5\times1)\div10=(2.5 + 1.5+1.5 + 1.5+1.5+2.5)\div10 = 11\div10 = 1.1\)

Answer:

Lin was better at estimating the mass of the objects because Lin has a lower MAD (225 grams) compared to Clare's MAD (275 grams), which means Lin's estimates were on average closer to the actual mass of 2000 grams for each object.