1

Earthquakes with a magnitude 7 to 7.9 are considered major

earthquakes. Earthquakes with magnitude larger than 8 are

considered great earthquakes. How frequently do these large

earthquakes occur?

SSAC2006.QE531.LV1.6

Frequency of Large Earthquakes

Introducing Some Elementary Statistical Descriptors

Prepared for SSAC byLen Vacher – University of South Florida

© The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. xxxx

Supporting quantitative concepts/skillsMean, median, modeVariance, standard deviationPercentiles, QuartilesInterpolationNormal distribution

Core Quantitative IssueData analysis: Exploratory statistical descriptors

2

Preview

The mission of the U.S. Geological Survey National Earthquake Information Center (USGS NEIC) is “to determine rapidly the location and size of all destructive earthquakes worldwide and to immediately disseminate this information to concerned national and international agencies, scientists, and the general public” (End note 1). The NEIC now locates some 50 earthquakes a day, or about 20,000 per year

Slide 3 gives some background on earthquake frequency and magnitude.

Slide 4 presents the 30 years of data that you will study: the number of large earthquakes per year for 1970-1999.

Slides 5-9 ask you for the mean; the variance and standard deviation; the maximum, minimum and range; the modes; and the median and quartiles of the data.

Slides 10 and 11 look at the quartiles more closely – in terms of percentiles. Linear interpolation becomes relevant in Slide 11.

Slides 12-14 ask you to plot the percentiles. In particular, Slide 14 asks you to consider the distribution of the data. How does the relation between the key percentiles and the standard deviation compare to that of the normal distribution?

Slide 15 wraps up, and Slide 16 gives you the end-of-module assignments, which involve data from 1940-1969.

3

Background on earthquake magnitude and frequency

B C D E F G H I2 Magnitude 2000 2001 2002 2003 2004 2005 2006*34 8.0 to 9.9 1 1 0 1 2 1 05 7.0 to 7.9 14 15 13 14 14 10 96 6.0 to 6.9 158 126 130 140 141 144 1047 5.0 to 5.9 1345 1243 1218 1203 1515 1699 11408 4.0 to 4.9 8045 8084 8584 8462 10888 13917 97369 3.0 to 3.9 4784 6151 7005 7624 7932 9173 753510 2.0 to 2.9 3758 4162 6419 7727 6316 4638 301411 1.0 to 1.9 1026 944 1137 2506 1344 26 1412 0.1 to 0.9 5 1 10 134 103 0 213 No Magnitude 3120 2938 2937 3608 2939 867 5411415 Total 22,256 23,534 27,454 31,419 31,194 30,475 22,0951617 Deaths (estimated) 231 21,357 1685 33,819 284,010 89,354 6595

U.S. Geological Survey National Earthquake Information Center, 11/6/2006

To appreciate the size of the large earthquakes, remember this: A magnitude-8 earthquake releases about 32× as much energy as a magnitude-7 earthquake, and a magnitude-7 earthquake releases about 32× as much energy as a magnitude-6 earthquake. Therefore a magnitude-8 earthquake is about 1000× as strong as a magnitude-6 earthquake. (End note 3)

As shown in the following table, there were 10-15 major and one great earthquake per year in 2000-2005. Over that period of time, five of the major earthquakes and none of the great earthquakes were in the US. (End note 2)

4

Problem

Here are the data. Start your spreadsheet by copying the

data in Columns B and C, starting with Row 3, as shown.

Data are from the Quantitative Environmental Learning Project (QELP), an NSF-sponsored project to promote quantitative reasoning using real data, by Greg Langkamp and Joe Hull of Seattle Central Community College. For information about this data set see http://www.seattlecentral.org/qelp/sets/039/039.html

• What are the mean, median, and mode of these data?• What are the variance and standard deviation?• What are the quartiles?• What are the 10th and 90th percentiles?

B C2 Yr Nbr3 1970 294 1971 235 1972 206 1973 167 1974 218 1975 219 1976 25

10 1977 1611 1978 1812 1979 1513 1980 1814 1981 1415 1982 1016 1983 1517 1984 818 1985 1519 1986 620 1987 1121 1988 822 1989 723 1990 1324 1991 1025 1992 2326 1993 1627 1994 1528 1995 2529 1996 2230 1997 2031 1998 1632 1999 11

5

Finding the Mean

With pencil and paper, one can count the number of data

(Cell F6), sum the total number of earthquakes (F8), and divide the second result

by the first (F10).

Excel does these steps easily.• Cell equation for F6:

=COUNT(C3:C32)• Cell equation for F8:

=SUM(C3:C32)

Delete one of the values in Column C, and replace another one with a letter. Then try these variations.• =COUNTA(C3:C32) • =SUMA(C3:C32)• =AVERAGEA(C3:C32)Explain what you observe (End note 4)

B C D E F2 Yr Nbr3 1970 294 1971 235 1972 206 1973 16 Nbr yrs 307 1974 218 1975 21 Sum Earthquakes 4879 1976 25

10 1977 16 Average Nbr per yr 16.211 1978 1812 1979 1513 1980 18 By Excel14 1981 1415 1982 10 Average 16.216 1983 1517 1984 818 1985 1519 1986 620 1987 1121 1988 822 1989 723 1990 1324 1991 1025 1992 2326 1993 1627 1994 1528 1995 2529 1996 2230 1997 2031 1998 1632 1999 11

Even easier – Cell equation for F15:

=AVERAGE(C3:C32)

6

Finding the variance and standard deviation

With pencil and paper, one calculates the deviation of each of the values from the average (Col E) and then squares each of them (Col F). The average of all of the deviations is zero (Cell I5). The average of all of the squared deviations is the population variance (I7). The square root of the population variance is the population standard deviation (I9). Using Excel’s built-in functions:=VARP(C3:C32)=STDEVP(C3:C32)

Without the “p”, VAR and STDEV return the sample variance and sample standard deviation, respectively. (End note 5)

Google research: What’s the difference between sample and population standard deviation?

B C D E F G H I

2 Yr Nbr DeviationDeviation-squared

3 1970 29 12.8 1634 1971 23 6.8 465 1972 20 3.8 14 average of deviations 0.06 1973 16 -0.2 07 1974 21 4.8 23 average of dev'ns-sqred 33.48 1975 21 4.8 239 1976 25 8.8 77 sqrt of avg of dev-sqred 5.7810 1977 16 -0.2 011 1978 18 1.8 312 1979 15 -1.2 2 By Excel13 1980 18 1.8 314 1981 14 -2.2 5 population variance 33.415 1982 10 -6.2 39 sample variance 34.516 1983 15 -1.2 217 1984 8 -8.2 68 population stdev 5.7818 1985 15 -1.2 2 sample stdev 5.8819 1986 6 -10.2 10520 1987 11 -5.2 2721 1988 8 -8.2 6822 1989 7 -9.2 8523 1990 13 -3.2 1024 1991 10 -6.2 3925 1992 23 6.8 4626 1993 16 -0.2 027 1994 15 -1.2 228 1995 25 8.8 7729 1996 22 5.8 3330 1997 20 3.8 1431 1998 16 -0.2 032 1999 11 -5.2 27

Recreate this spreadsheet.

7

Finding the range

With pencil and paper, one sorts the data from highest to lowest and then reads off the largest and smallest values, as well as the second largest and third smallest values, if you wish. The range is the largest value minus the smallest value (29 – 6, in this case).

To sort in Excel: • Copy the block to be sorted (B3 to C32) to a blank part of the spreadsheet (E3 to F32).• Block out E3 to F32.• Select “Data” on tool bar• Select “Sort”• Choose Column F and “Descending”• Choose OK

Excel’s built-in functions:• For Max

=MAX(C3:C32)• For minimum

=MIN(C3:C32) (End note 6)• For 2nd largest

=LARGE(C3:C32,2)• For 3rd smallest

=SMALL(C3:C32,3)

B C D E F G H I2 Yr Nbr Ordered3 1970 29 1970 29 <<<Max4 1971 23 1976 25 <<<Second largest5 1972 20 1995 256 1973 16 1971 23 <<<Third7 1974 21 1992 238 1975 21 1996 229 1976 25 1974 21

10 1977 16 1975 21 By Excel11 1978 18 1972 2012 1979 15 1997 20 Max 2913 1980 18 1978 18 2nd 2514 1981 14 1980 18 3rd 2515 1982 10 1973 1616 1983 15 1977 16 Min 617 1984 8 1993 16 2nd 718 1985 15 1998 16 3rd 819 1986 6 1979 1520 1987 11 1983 15 Range 2321 1988 8 1985 1522 1989 7 1994 1523 1990 13 1981 1424 1991 10 1990 1325 1992 23 1987 1126 1993 16 1999 1127 1994 15 1982 1028 1995 25 1991 1029 1996 22 1984 830 1997 20 1988 8 <<<Third31 1998 16 1989 7 <<<Second smallest32 1999 11 1986 6 <<<Min

8

Finding modes

When the data are sorted, one can count the number of times that each value occurs. Column G provides these counts. Cell G3, for example, says that there was one year with 29 earthquakes, and G6 says that there were two years with 25 earthquakes. The most frequent values are 16 (4 times) and 15 (4 times). Thus 15 and 16 are modes (a composite mode).

Excel’s built-in functions – • For mode (J8):

=MODE(C3:C32)

For counts – • For number of times the value is 16:

=COUNTIF(C3:C32,16)• For number of times value is larger than 16:

=COUNTIF(C3:C32,”>16”)• For number of times value is 16 or larger:

=COUNTIF(C3:C32,”>=16”)• For number of times value is not 16:

=COUNTIF(C3:C32,”<>16”)The SUMIF function works the same way as the COUNTIF function

B C D E F G H I J2 Yr Nbr Ordered Counting3 1970 29 1970 29 14 1971 23 1976 25 25 1972 20 1995 256 1973 16 1971 23 2 By Excel7 1974 21 1992 238 1975 21 1996 22 1 Mode 169 1976 25 1974 21 2

10 1977 16 1975 21 Nbr of 16s 411 1978 18 1972 20 212 1979 15 1997 20 Nbr of 15s 413 1980 18 1978 18 2 Nbr of 19s 014 1981 14 1980 1815 1982 10 1973 16 4 Nbr >16 1216 1983 15 1977 16 Nbr>=16 1617 1984 8 1993 16 Nbr <16 1418 1985 15 1998 16 Nbr<=16 1819 1986 6 1979 15 4 Nbr not 16 2620 1987 11 1983 1521 1988 8 1985 15 Nbr 14-18 1122 1989 7 1994 1523 1990 13 1981 14 124 1991 10 1990 13 1 Sumifs25 1992 23 1987 11 2 Sum if 16 6426 1993 16 1999 11 Sum if >=16 32927 1994 15 1982 10 228 1995 25 1991 1029 1996 22 1984 8 230 1997 20 1988 831 1998 16 1989 7 132 1999 11 1986 6 1

Recreate this spreadsheet.

9

Finding quartiles

When the data are sorted, one can locate the median and quartiles. The median is the value that occurs halfway through the list. For 30 values, the halfway position is 31/2 – in in general (COUNT+1)/2 (J6). The first quartile occurs a quarter of the way through from the bottom – or at (COUNT+1)/4 (J7), and the third quartile occurs three- quarters of the way through – or at (COUNT+1)*3/4 (J8).

The horizontal boxes from Column F to H identify the quartiles from this sorting: 11 for the first quartile (Q1), 16 for the second quartile (Q2 or median), and 21 for the third quartile (Q3).

Excel’s built-in functions – • For median (J12)):

=MEDIAN(C3:C32) For Q1 (J13):

=QUARTILE(C3:C32,1)• For Q2 (J14):

=QUARTILE(C3:C32,2)• For Q3 (J15)::

=QUARTILE(C3:C32,3)NOTE: The results (J13, J15) do not agree with our values from counting through our sorted list. What is EXCEL doing?

Another way that quartiles are determined is:• Q1 is the median of the smaller half of the list – MEDIAN(G18:G32)• Q3 is the median of the larger half of the list – MEDIAN(G3:G17)NOTE: These results (J21 and J22) don’t agree with Excel’s built-in functions either.

B C D E F G H I J2 Yr Nbr Ordered Rank3 1970 29 1970 29 14 1971 23 1976 25 25 1972 20 1995 25 3 Count 306 1973 16 1971 23 4 mid count 15.57 1974 21 1992 23 5 1st qtr count 7.758 1975 21 1996 22 6 3rd qtr count 23.259 1976 25 1974 21 7 Upr Qtr10 1977 16 1975 21 811 1978 18 1972 20 9 By Excel12 1979 15 1997 20 10 median 1613 1980 18 1978 18 11 Q1 11.514 1981 14 1980 18 12 Q2 1615 1982 10 1973 16 13 Q3 20.7516 1983 15 1977 16 1417 1984 8 1993 16 15 Mid-Count18 1985 15 1998 16 1619 1986 6 1979 15 17 By Excel20 1987 11 1983 15 18 median 1621 1988 8 1985 15 19 med(upr half) 2122 1989 7 1994 15 20 med(lwr half) 1123 1990 13 1981 14 2124 1991 10 1990 13 2225 1992 23 1987 11 23 Lwr Qtr26 1993 16 1999 11 2427 1994 15 1982 10 2528 1995 25 1991 10 2629 1996 22 1984 8 2730 1997 20 1988 8 2831 1998 16 1989 7 2932 1999 11 1986 6 30

10

Finding percentiles and comparing them to quartiles

Excel uses percentiles to calculate quartiles. The median is the 50th percentile, meaning that 50% of the data are smaller than the median. Q1 is the 25th percentile, meaning that 25% of the data are smaller than Q1. Q3 is the 75th percentile, meaning that 75% of the data are smaller than Q3

One can calculate the percentile of each position in the sorted list (Column H). Cell H4 shows that the second highest position contains the 96.6th percentile. It is calculated as (29-1)/(30-1) or in Excel

=(G4-1)/(COUNT($C$3:$C$32)-1)

The $-symbols are included in order that the equation can be copied through Column H.

The 75th percentile clearly occurs between 20 and 21, and closer to 21.The 25th percentile clearly occurs between 11 and 13, and closer to 11.Both observations are consistent with the values returned by Excel for Q3 and Q1, respectively.What do we find if we interpolate?

B C D E F G H I J K

2 Yr Nbr

Ordered largest at

top

Rank from

bottom Percentile3 1970 29 1970 29 30 1.0004 1971 23 1976 25 29 0.9665 1972 20 1995 25 28 0.9316 1973 16 1971 23 27 0.8977 1974 21 1992 23 26 0.8628 1975 21 1996 22 25 0.8289 1976 25 1974 21 24 0.793 Excel10 1977 16 1975 21 23 0.759 75th vs 20.7511 1978 18 1972 20 22 0.72412 1979 15 1997 20 21 0.69013 1980 18 1978 18 20 0.65514 1981 14 1980 18 19 0.62115 1982 10 1973 16 18 0.58616 1983 15 1977 16 17 0.55217 1984 8 1993 16 16 0.517 50th vs 1618 1985 15 1998 16 15 0.48319 1986 6 1979 15 14 0.44820 1987 11 1983 15 13 0.41421 1988 8 1985 15 12 0.37922 1989 7 1994 15 11 0.34523 1990 13 1981 14 10 0.31024 1991 10 1990 13 9 0.276 25th vs 11.525 1992 23 1987 11 8 0.24126 1993 16 1999 11 7 0.20727 1994 15 1982 10 6 0.17228 1995 25 1991 10 5 0.13829 1996 22 1984 8 4 0.10330 1997 20 1988 8 3 0.06931 1998 16 1989 7 2 0.03432 1999 11 1986 6 1 0.000

11

Finding quartiles by interpolating percentiles

Cell equation in J10:=F11+(.75-H11)/(H10-H11)*(F10-F11)

Why? Explain using the word

proportion.

What cell equations

belong in J17 and J24?

It looks like Excel determines quartiles as

percentiles by interpolation.

For Excel’s algorithm see: http://support.microsoft.com/?kbid=214072

B C D E F G H I J K

2 Yr Nbr

Ordered largest at

top

Rank from

bottom Percentile Interpolate Excel3 1970 29 1970 29 30 1.0004 1971 23 1976 25 29 0.9665 1972 20 1995 25 28 0.9316 1973 16 1971 23 27 0.8977 1974 21 1992 23 26 0.8628 1975 21 1996 22 25 0.8289 1976 25 1974 21 24 0.793

10 1977 16 1975 21 23 0.759 75th 20.75 20.7511 1978 18 1972 20 22 0.72412 1979 15 1997 20 21 0.69013 1980 18 1978 18 20 0.65514 1981 14 1980 18 19 0.62115 1982 10 1973 16 18 0.58616 1983 15 1977 16 17 0.55217 1984 8 1993 16 16 0.517 50th 16 1618 1985 15 1998 16 15 0.48319 1986 6 1979 15 14 0.44820 1987 11 1983 15 13 0.41421 1988 8 1985 15 12 0.37922 1989 7 1994 15 11 0.34523 1990 13 1981 14 10 0.31024 1991 10 1990 13 9 0.276 25th 11.5 11.525 1992 23 1987 11 8 0.24126 1993 16 1999 11 7 0.20727 1994 15 1982 10 6 0.17228 1995 25 1991 10 5 0.13829 1996 22 1984 8 4 0.10330 1997 20 1988 8 3 0.06931 1998 16 1989 7 2 0.03432 1999 11 1986 6 1 0.000

12

Graphing the percentiles

To visualize what we have done by interpolation, plot percentile (Col G) against earthquakes per year (Col E) and see where the 25, 50 and 75 percentiles cross

the data curve. Increase the y-scale to see the crossings more clearly.

B C D E F G H I J K L M N

2 Yr Nbr

Ordered largest at

top

Rank from

bottom Percentile3 1970 29 1970 29 30 1.0004 1971 23 1976 25 29 0.9665 1972 20 1995 25 28 0.9316 1973 16 1971 23 27 0.8977 1974 21 1992 23 26 0.8628 1975 21 1996 22 25 0.8289 1976 25 1974 21 24 0.793

10 1977 16 1975 21 23 0.75911 1978 18 1972 20 22 0.72412 1979 15 1997 20 21 0.69013 1980 18 1978 18 20 0.65514 1981 14 1980 18 19 0.62115 1982 10 1973 16 18 0.58616 1983 15 1977 16 17 0.55217 1984 8 1993 16 16 0.51718 1985 15 1998 16 15 0.48319 1986 6 1979 15 14 0.44820 1987 11 1983 15 13 0.41421 1988 8 1985 15 12 0.37922 1989 7 1994 15 11 0.34523 1990 13 1981 14 10 0.31024 1991 10 1990 13 9 0.27625 1992 23 1987 11 8 0.24126 1993 16 1999 11 7 0.20727 1994 15 1982 10 6 0.17228 1995 25 1991 10 5 0.13829 1996 22 1984 8 4 0.10330 1997 20 1988 8 3 0.06931 1998 16 1989 7 2 0.03432 1999 11 1986 6 1 0.000

Earthquakes >M7, 1970-1999

0.000

0.250

0.500

0.750

1.000

5 10 15 20 25 30

number of EQs in year

pe

rce

nti

le

13

Graphing the percentiles (2)

How does the graph on this slide differ from the graph on Slide 12?

B C D E F G H I J K L M

2 Yr Nbr percentilenumber per year

percentile (for graph)

3 1970 294 1971 23 1.00 29 1.005 1972 20 0.95 25 0.956 1973 16 0.90 23.2 0.907 1974 21 0.85 22.65 0.858 1975 21 0.80 21.2 0.809 1976 25 0.75 20.75 0.75

10 1977 16 0.70 20 0.7011 1978 18 0.65 18 0.6512 1979 15 0.60 16.8 0.6013 1980 18 0.55 16 0.5514 1981 14 0.50 16 0.5015 1982 10 0.45 15.05 0.4516 1983 15 0.40 15 0.4017 1984 8 0.35 15 0.3518 1985 15 0.30 13.7 0.3019 1986 6 0.25 11.5 0.2520 1987 11 0.20 10.8 0.2021 1988 8 0.15 10 0.1522 1989 7 0.10 8 0.1023 1990 13 0.05 7.45 0.0524 1991 10 0.00 6 0.0025 1992 2326 1993 1627 1994 1528 1995 2529 1996 2230 1997 2031 1998 1632 1999 11

Cumulated Frequency of EQs >M7

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 5 10 15 20 25 30

Number of earthquakes per year

Pe

rce

nti

le

Or, instead of interpolating, use Excel’s built-in function to find whatever percentile you want. For example, Column E lists percentiles incrementally.

Column F lists the corresponding percentiles – cell equation for F5 is =PERCENTILE($C$3:$C$32,E5). The $-symbols are included so you can copy

the formula through the column. Column G repeats Column E so you can easily plot the graph as Column G vs. Column F (End note 7).

14

Key percentiles

Recreate this spreadsheet. Column E lists the key

percentiles. Column F uses the PERCENTILE function. The cell equation for H6 is (F6-F8)/STDEVP(C3:C32)/2. The graph plots Column E

against Column F.

A normal distribution has the property that 68.2% of

the values lie within plus or minus one standard

deviation of the mean (i.e., between percentiles of

84.1% and 15.9%). Similarly, 95.4% and 99.7% of the values are within +/-

two and three standard deviations, respectively, in a normal distribution. How

do these standards compare to the distribution of earthquakes per year?

H6, I5, and J4 would be 1.00, 2.00, and 3.00 respectively if the earthquakes per year were distributed normally. This is good agreement. The distribution of earthquakess per year is nearly normal.

B C D E F G H I J K

2 Yr Nbr percentilenumber per year

central 68.2% (+/- STDEVP

units)

central 95.4% (+/- STDEVP

units

central 99.7% +/- STDEVP

units3 1970 294 1971 23 0.999 28.884 1.985 1972 20 0.977 26.332 1.706 1973 16 0.841 22.389 1.077 1974 21 0.500 168 1975 21 0.159 109 1976 25 0.023 6.667

10 1977 16 0.001 6.02911 1978 1812 1979 1513 1980 1814 1981 1415 1982 1016 1983 1517 1984 818 1985 1519 1986 620 1987 1121 1988 822 1989 723 1990 1324 1991 1025 1992 2326 1993 1627 1994 1528 1995 2529 1996 2230 1997 2031 1998 1632 1999 11

0.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30

Number Earthquakes per Year

Per

cent

ile

15

What we have found for 1970-1999

B C2 Yr Nbr3 1970 294 1971 235 1972 206 1973 167 1974 218 1975 219 1976 25

10 1977 1611 1978 1812 1979 1513 1980 1814 1981 1415 1982 1016 1983 1517 1984 818 1985 1519 1986 620 1987 1121 1988 822 1989 723 1990 1324 1991 1025 1992 2326 1993 1627 1994 1528 1995 2529 1996 2230 1997 2031 1998 1632 1999 11

Number of Earthquakes (M>7) per Year, 1970-1999

• On average there were 16.2 large (M>7) earthquakes per year. (Read this as 162 in ten years if you don’t like the notion of 0.2 earthquakes in a year.)• The standard deviation was 15.7 earthquakes per year.• The median was 16, which was also a mode.• The distribution was unimodal: there were four years with 16 earthquakes and four with 15.• The maximum number was 29 (1970), and the minimum was 6 (1986) giving a total range of 23.• Q3 was 20.75 and Q1 was 11.5 giving an interquartile range (Q3-Q1) of 9.25 earthquakes per year.• The 90th percentile was 23.2, and the 10th percentile was 8.0, meaning the range of the central 80% of the distribution was 14.2 earthquakes per year. • The central 68.2% of the distribution occurred within +/- 1.1 standard deviations of the mean, and the central 95.4%, within 1.7 standard deviations of the mean. On this basis the distribution of earthquakes per year was nearly normal.

16

End of Module Assignments

B C2 Year Nbr3 1940 234 1941 245 1942 276 1943 417 1944 318 1945 279 1946 35

10 1947 2611 1948 2812 1949 3613 1950 2914 1951 2115 1952 1716 1953 2217 1954 1718 1955 1919 1956 1520 1957 3421 1958 1022 1959 1523 1960 2224 1961 1825 1962 1526 1963 2027 1964 1528 1965 2229 1966 1930 1967 1631 1968 3032 1969 27

Here are the data from the preceding thirty years, 1940-1969, from the QELP Data Set 039: http://www.seattlecentral.org/qelp/sets/039/039.html

1. Rewrite the information of Slide 15 replacing the statistics with numbers appropriate to the 1940-1969 data. Use bullets in the same order so that your answers are easy to grade. If you can, use a PowerPoint slide (simply copy and paste Slide 15 into a new presentation, delete the data set, and change the numbers in the bulleted items appropriately).

2. Hand in spreadsheets for Slides 6, 8, 12 and 13 for the new data set. Include the graphs for the last two.

3. Answer the questions in the green boxes of Slides 5, 11 and 13.

4. Find the mean, median, standard deviation and quartiles for the sixty years of data. Find the +/- number of standard deviations for the central 68.2%, 95.4% and 99.7% of the sixty years of data (Slide 14).

5. Based on the information in this module – a. What is the standard deviation and why is it important?b. What are quartiles and why are they important?c. What are percentiles and why are they important?

17

End notes

1. Home page: http://earthquake.usgs.gov/regional/neic/. Return to Slide 2.

2. For earthquake facts and statistics see the USGS NEIC Website: http://neic.usgs.gov/neis/eqlists/eqstats.html. Return to Slide 3.

3. How large is an 8.7-magnitude earthquake compared to a magnitude-5.8 earthquake? See the USGS Website: http://earthquake.usgs.gov/learning/topics/how_much_bigger.php. Return to Slide 3.

4. Experiment also with the function COUNTBLANK(array). Return to Slide 5.

5. As variations on the COUNTA(array) theme, there are also the following built-in functions: VARA(array), VARPA(array), STDEVA(array), STDEVPA(array). Return to Slide 6.

6. There are also MAXA(array) and MINA(array). Return to Slide 7.

7. Or if you want to reverse the axes (i.e., plot x vs. y, instead of y vs. x), here is one way of doing it. Plot y vs. x as usual. Right-click on the gray area of the graph. Select “Source data …” from the popup window. Select the “Series” tab. Click on the small icon to the right of the X-values. The address of your x-series will appear in a long, skinny window and a shimmering outline will appear around the series block in the spreadsheet. Change the address in the skinny window to that of the Y-values. One easy way of doing that is to use the mouse to outline the block of the Y-values on the spreadsheet. Notice how the address in the skinny window changes as you move the mouse down the column. When the block is the size you want, release the mouse button and hit enter. Repeat for the Y-values, replacing their address with the address of the old X-values. Rescale and retitle the axes. Return to Slide 13.