Math Problem Statement

Simpangan rata-rata dari data 4,5,6,7,8 adalah...

Solution

The problem asks for the "simpangan rata-rata" (mean deviation) of the data set 4,5,6,7,84, 5, 6, 7, 8.

Steps to calculate the mean deviation:

  1. Calculate the mean of the data set: Mean=4+5+6+7+85=305=6\text{Mean} = \frac{4 + 5 + 6 + 7 + 8}{5} = \frac{30}{5} = 6

  2. Find the absolute deviations from the mean: 46=2,56=1,66=0,76=1,86=2|4 - 6| = 2, \quad |5 - 6| = 1, \quad |6 - 6| = 0, \quad |7 - 6| = 1, \quad |8 - 6| = 2

  3. Calculate the mean of the absolute deviations (mean deviation): Mean deviation=2+1+0+1+25=65=1.2\text{Mean deviation} = \frac{2 + 1 + 0 + 1 + 2}{5} = \frac{6}{5} = 1.2

So, the mean deviation is 1.2.

Answer: D. 1,21,2

Would you like more details or have any questions?

Related Questions:

  1. How would the mean deviation change if the data set was 3,4,5,6,73, 4, 5, 6, 7?
  2. What is the difference between mean deviation and standard deviation?
  3. How can you calculate the mean deviation for a larger data set?
  4. Why is it necessary to use absolute values when calculating mean deviation?
  5. What are the implications of having a high or low mean deviation in a data set?

Tip: Mean deviation is a simple way to measure the variability in a data set. Always ensure to use absolute values to avoid negative deviations canceling out the positive ones.

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Math Problem Analysis

Mathematical Concepts

Mean Deviation
Arithmetic Mean

Formulas

Mean = (Sum of Data Points) / (Number of Data Points)
Mean Deviation = (Sum of Absolute Deviations) / (Number of Data Points)

Theorems

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Suitable Grade Level

Grades 7-9