Answer:
Explanation:
Hello!
The data below shows the magnitude values of 50 earthquakes:
2,53; 0,64; 0,67; 1,61; 2,06; 2,01; 1,98; 1,01; 1,52; 1,53; 0,14; 0,01; 0,81; 0,08; 0,74; 1,77; 0,35; 2,77; 0,01; 1,62; 2,77; 1,45; 2,66; 1,58; 2,03; 1,33; 2,55; 0,57; 0,69; 1,84; 2,74; 0,99; 2,59; 1,41; 0,92; 1,15; 2,02; 1,48; 1,16; 0,24; 2,74; 0,65; 1,04; 2,31; 2,91; 2,41; 2,06; 1,73; 0,82; 1,78
To calculate the mean you have to add all observations and divide it by the sample size:
X[bar]= ∑X/n= 74.48/50= 1.4896≅ 1.49
To find the median you have to calculate its position:
PosMe: n/2= 50/2= 25
The median is the observation in the 25th place, so you have to order the data from least to greatest and identify the 25th observation:
0,01; 0,01; 0,08; 0,14; 0,24; 0,35; 0,57; 0,64; 0,65; 0,67; 0,69; 0,74; 0,81; 0,82; 0,92; 0,99; 1,01; 1,04; 1,15; 1,16; 1,33; 1,41; 1,45; 1,48; 1,52; 1,53; 1,58; 1,61; 1,62; 1,73; 1,77; 1,78; 1,84; 1,98; 2,01; 2,02; 2,03; 2,06; 2,06; 2,31; 2,41; 2,53; 2,55; 2,59; 2,66; 2,74; 2,74; 2,77; 2,77; 2,91
Me= 1.52
An outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on a statistical analysis.
Any value that is ± 3 standard deviations from the mean can be considered an outlier.
If the standard deviation for this data set is S= 0.84
Any value below X[bar]-3*S= 1.49-3*0.84= -1.03
Or any value above X[bar]+3*S= 1.49+3.0.84= 4.01
Can be considered an outlier. So for this data set, an earthquake with magnitude 7.0 on the Richter scale can be considered an outlier.
I hope this helps!