4. 5. 6. 1: More Info Use the magnitudes (Richter scale) of the earthquakes listed in the data set below. Find the mean and median of this data set. Is the magnitude of an earthquake measuring 7.0 on the Richter scale an outlier (data value that is very far away from the others) when considered in the context of the sample data given in this data set? Explain. Click the icon to view the earthquake Richter scale data

Step-by-step 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!

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15