Measurement and Data>Calculating Mean Absolute Deviation to Describe Data Variation(TEKS.Math.8.11.B)
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Texas 8th Grade Math › Measurement and Data>Calculating Mean Absolute Deviation to Describe Data Variation(TEKS.Math.8.11.B)
Questions 1 - 5
1
What is the MAD of these scores, rounded to the nearest tenth? 12, 15, 14, 10, 18, 16, 11, 14
0
8
2
2
Explanation
- Find the mean: $\frac{12+15+14+10+18+16+11+14}{8}=\frac{110}{8}=13.75$. 2) Find absolute deviations: $|12-13.75|=1.75$, $|15-13.75|=1.25$, $|14-13.75|=0.25$, $|10-13.75|=3.75$, $|18-13.75|=4.25$, $|16-13.75|=2.25$, $|11-13.75|=2.75$, $|14-13.75|=0.25$. Sum $=16.5$. 3) Mean of deviations: $\frac{16.5}{8}=2.0625\approx 2.1$.
2
What is the MAD of these scores, rounded to the nearest tenth? 5, 9, 7, 6, 10, 8, 5
5
2
0
2
Explanation
- Find the mean: $\frac{5+9+7+6+10+8+5}{7}=\frac{50}{7}\approx 7.1429$. 2) Absolute deviations: $|5-7.1429|\approx 2.1429$, $|9-7.1429|\approx 1.8571$, $|7-7.1429|\approx 0.1429$, $|6-7.1429|\approx 1.1429$, $|10-7.1429|\approx 2.8571$, $|8-7.1429|\approx 0.8571$, $|5-7.1429|\approx 2.1429$. Sum $\approx 11.1429$. 3) Mean of deviations: $\frac{11.1429}{7}\approx 1.5918\approx 1.6$.
3
What is the MAD of these scores, rounded to the nearest tenth? 20, 22, 19, 21, 25, 18, 24, 20, 23, 17
2
0
8
2
Explanation
- Find the mean: $\frac{209}{10}=20.9$. 2) Absolute deviations: $|20-20.9|=0.9$, $|22-20.9|=1.1$, $|19-20.9|=1.9$, $|21-20.9|=0.1$, $|25-20.9|=4.1$, $|18-20.9|=2.9$, $|24-20.9|=3.1$, $|20-20.9|=0.9$, $|23-20.9|=2.1$, $|17-20.9|=3.9$. Sum $=21.0$. 3) Mean of deviations: $\frac{21.0}{10}=2.1$.
4
What is the MAD of these scores, rounded to the nearest tenth? 32, 28, 30, 35, 27, 33
8
0
3
3
Explanation
- Find the mean: $\frac{32+28+30+35+27+33}{6}=\frac{185}{6}\approx 30.8333$. 2) Absolute deviations: $|32-30.8333|\approx 1.1667$, $|28-30.8333|\approx 2.8333$, $|30-30.8333|\approx 0.8333$, $|35-30.8333|\approx 4.1667$, $|27-30.8333|\approx 3.8333$, $|33-30.8333|\approx 2.1667$. Sum $\approx 15.0$. 3) Mean of deviations: $\frac{15.0}{6}=2.5$.
5
What is the MAD of these scores, rounded to the nearest tenth? 41, 45, 39, 44, 42, 38, 47, 40, 43
0
9
3
2
Explanation
- Find the mean: $\frac{41+45+39+44+42+38+47+40+43}{9}=\frac{379}{9}\approx 42.1111$. 2) Absolute deviations: $|41-42.1111|\approx 1.1111$, $|45-42.1111|\approx 2.8889$, $|39-42.1111|\approx 3.1111$, $|44-42.1111|\approx 1.8889$, $|42-42.1111|\approx 0.1111$, $|38-42.1111|\approx 4.1111$, $|47-42.1111|\approx 4.8889$, $|40-42.1111|\approx 2.1111$, $|43-42.1111|\approx 0.8889$. Sum $\approx 21.1111$. 3) Mean of deviations: $\frac{21.1111}{9}\approx 2.3457\approx 2.3$.