Question

shelley started doing sit - ups to prepare for the school fitness test. on 10 days she did: 22 sit - ups, 54 sit - ups, 34 sit - ups, 57 sit - ups, 36 sit - ups, 59 sit - ups, 14 sit - ups, 16 sit - ups, 46 sit - ups, 73 sit - ups. what was the mean absolute deviation of the numbers of sit - ups she did? if the answer is a decimal, round it to the nearest tenth. mean absolute deviation (mad): sit - ups

Explanation:

Step1: Calculate the mean

The data set is \(22,54,34,57,36,59,14,16,46,73\).
The sum of the data is \(22 + 54+34 + 57+36+59+14+16+46+73=411\).
The number of data - points \(n = 10\).
The mean \(\bar{x}=\frac{411}{10}=41.1\).

Step2: Calculate the absolute deviations

\(\vert22 - 41.1\vert=19.1\), \(\vert54 - 41.1\vert = 12.9\), \(\vert34 - 41.1\vert=7.1\), \(\vert57 - 41.1\vert = 15.9\), \(\vert36 - 41.1\vert=5.1\), \(\vert59 - 41.1\vert = 17.9\), \(\vert14 - 41.1\vert=27.1\), \(\vert16 - 41.1\vert = 25.1\), \(\vert46 - 41.1\vert=4.9\), \(\vert73 - 41.1\vert = 31.9\).

Step3: Calculate the sum of absolute deviations

The sum of absolute deviations is \(19.1+12.9+7.1+15.9+5.1+17.9+27.1+25.1+4.9+31.9 = 167\).

Step4: Calculate the mean absolute deviation

The mean absolute deviation \(MAD=\frac{167}{10}=16.7\).

Answer:

16.7