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QuestionCalculate the mean absolute deviation of the values 4, 15, 16, 7, 5, 19. Round to the nearest hundredth if needed.

Studdy Solution

STEP 1

Assumptions1. The data set contains the following values4,15,16,7,5,19. We need to find the mean absolute deviation (MAD) of this data set3. If necessary, we will round the final answer to the nearest hundredth

STEP 2

First, we need to find the mean (average) of the data set. The mean is calculated by summing all the values in the data set and then dividing by the number of values.
Mean=Sum of all valuesNumber of valuesMean = \frac{Sum\, of\, all\, values}{Number\, of\, values}

STEP 3

Now, plug in the given values to calculate the mean.
Mean=+15+16+7+5+196Mean = \frac{ +15 +16 +7 +5 +19}{6}

STEP 4

Calculate the mean.
Mean=666=11Mean = \frac{66}{6} =11

STEP 5

Next, we need to find the absolute deviations of each data point from the mean. The absolute deviation is the absolute value of the difference between each data point and the mean.
Absolute deviation=∣Data point−Mean∣Absolute\, deviation = |Data\, point - Mean|

STEP 6

Calculate the absolute deviations for each data point.
For4 ∣4−11∣=|4 -11| =For15 ∣15−11∣=4|15 -11| =4For16 ∣16−11∣=5|16 -11| =5For ∣−11∣=4| -11| =4For5 ∣5−11∣=6|5 -11| =6For19 ∣19−11∣=8|19 -11| =8

STEP 7

Now that we have the absolute deviations, we can calculate the mean of these deviations. This is done by summing all the absolute deviations and then dividing by the number of values.
Mean absolute deviation=Sum of absolute deviationsNumber of valuesMean\, absolute\, deviation = \frac{Sum\, of\, absolute\, deviations}{Number\, of\, values}

STEP 8

Plug in the values for the sum of absolute deviations and the number of values to calculate the mean absolute deviation.
Mean absolute deviation=7+4+5+4+6+86Mean\, absolute\, deviation = \frac{7 +4 +5 +4 +6 +8}{6}

STEP 9

Calculate the mean absolute deviation.
Mean absolute deviation=346=5.67Mean\, absolute\, deviation = \frac{34}{6} =5.67The mean absolute deviation of the data set is5.67, rounded to the nearest hundredth.

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