Calculate the average deviation from the mean for the following dataset: {23,24,26,27,28,30,31}

Question

. Round your answer to the nearest hundredth.(1 point)
The average deviation from the mean is (give a solid number answer, no decimals )

Answer 1

To calculate the average deviation from the mean for the dataset {23, 24, 26, 27, 28, 30, 31}, follow these steps:

1. Calculate the mean of the dataset: $$\text{Mean}=\frac{23+24+26+27+28+30+31}{7}=\frac{189}{7}=27$$

2. Calculate the deviations from the mean:

   • Deviation for 23: $23-27=-4$
   • Deviation for 24: $24-27=-3$
   • Deviation for 26: $26-27=-1$
   • Deviation for 27: $27-27=0$
   • Deviation for 28: $28-27=1$
   • Deviation for 30: $30-27=3$
   • Deviation for 31: $31-27=4$

3. Take the absolute values of the deviations:

   • Absolute deviation for 23: $|-4|=4$
   • Absolute deviation for 24: $|-3|=3$
   • Absolute deviation for 26: $|-1|=1$
   • Absolute deviation for 27: $|0|=0$
   • Absolute deviation for 28: $|1|=1$
   • Absolute deviation for 30: $|3|=3$
   • Absolute deviation for 31: $|4|=4$

4. Sum the absolute deviations: $$4+3+1+0+1+3+4=16$$

5. Calculate the average deviation: $$\text{Average Deviation}=\frac{\text{Sum of Absolute Deviations}}{\text{Number of Data Points}}=\frac{16}{7}\approx 2.2857$$

6. Round to the nearest hundredth: $$\text{Average Deviation}\approx 2.29$$

Finally, since you requested a solid number answer without decimals, the final average deviation is:

2 (the integer part of 2.29).