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  • #1

    Syntax Missing value imputation for districts without stations

    Dear members of the Statalist forum,

    I have the following problem. Among other things, I am looking at temperature data from weather stations that I have matched with the corresponding electoral districts ( German federal election 2021) via geo-coordinates. The weather data is available daily (here simplified for two days: temp_a22312 and temp_a22313). I would like to use the temperature values of the three nearest weather stations to form a temperature average for those districts in which there are no stations (station==.) or which have missing values (districts_to_check==1). However, when I apply the code below, the exact same temperature values are calculated and applied for each missing district. I think this is because of the incorrectly formulated condition. However, after trying several times, I have not been able to find a solution. I would be very grateful for any help. The data looks like this. For example, there is no weather station located in districts 18, 19, 20..

    district closest_station1 closest_station2 closest_station3 station temp_a22312 temp_a22313
    1 1130 4466 1379 1266 -4.9 -4
    2 7298 4919 1963 4919 . .
    3 19172 2429 1451 2429 -4.6 -3.2
    4 6105 2303 2437 5930 -2 -3.3
    5 2564 2961 6105 2564 -2.9 -3.1
    6 6163 2564 2306 6163 -3.5 -3.2
    7 4039 1975 4857 2115 -2.7 -1.8
    8 5280 7427 4039 5280 -5 -3
    9 3897 5877 2306 5877 . .
    10 1736 591 3086 1736 -5.4 -2.4
    11 3086 5078 1736 3086 -5.3 -2.7
    12 4625 591 1736 591 -5.7 -2.6
    13 4625 1694 5624 1694 -3.8 -2.1
    14 1803 4271 2796 4271 -4.5 -2.3
    15 6199 298 5097 6199 -4.3 -2.2
    16 167 5142 5109 167 -4.4 -1.8
    17 5349 5009 15189 15189 . .
    18 1975 1981 2465 . . .
    19 2465 1981 1975 . . .
    20 1975 4039 1981 . . .
    21 1975 4039 1981 1975 -5.3 -2.5
    22 1975 1981 4039 . . .
    23 1981 760 1975 1981 -5.8 -2.4
    24 5839 5640 3631 5839 -5.8 -2.6
    25 3867 6159 1503 1792 -3.9 -2.3
    26 5640 6157 5344 5640 -5.9 -3
    27 1503 44 642 . . .
    28 642 44 691 44 -4.9 -2.1
    29 4841 3639 701 1451 -5 -3.3
    30 704 4857 5014 4857 -5.7 -2.6
    31 3640 3254 1792 3254 -3.9 -2.3
    use weather_data.dta, clear
    tab district if station==. // identify districts without station

    egen group_district = group(district)
    egen has_missing_tmk = max(missing(temp_a22312 - temp_a22312)), by(group_district) // Identify districts with stations having missing values on temp* variables
    egen has_data_tmk = max(temp_a22312 - temp_a22312 != .), by(group_district) // Identify districts with at least one station having data on temp* variables
    gen districts_to_check = has_missing_tmk & !has_data_tmk & station !=. //Identify districts that meet the criteria
    list district if districts_to_check

    local date_list 22312 22313

    levelsof district, local(district_list)

    foreach district of local district_list {
    gen closest_station1_`district' = closest_station1 if district == `district'
    gen closest_station2_`district' = closest_station2 if district == `district'
    gen closest_station3_`district' = closest_station3 if district == `district'
    }

    foreach district in `district_list' {
    foreach date in `date_list' {
    egen temp_avg`district'`date' = mean(temp_a`date') if (station == closest_station1_`district' | station == closest_station2_`district' | station == closest_station3_`district')
    replace temp_a`date' = temp_avg`district'`date' if (missing(temp_a`date')) & station==. | (missing(temp_a`date')) & districts_to_check==1
    }
    }
    The error seems to me to be in the last two lines of the command, as it is not possible in this way to calculate averages for districts to which no stations have been assigned. But as I already said, I have no solution to this.

    Best regards and thanks in advance,
    Jessica
    Tags: None
  • #2
    You are probably better off with a long data layout, in which case exclude the reshape wide command at the end of the code below. On framing:

    I would like to use the temperature values of the three nearest weather stations to form a temperature average for those districts in which there are no stations
    Not all 3 closest stations have weather data, so use the wording "up to three" to imply that if there are two stations available, only the two observations will be used and if there is one station, then that station's observation will be used.

    Code:
    * Example generated by -dataex-. To install: ssc install dataex
clear
input byte district int(closest_station1 closest_station2 closest_station3 station) float(temp_a22312 temp_a22313)
 1  1130 4466  1379  1266 -4.9   -4
 2  7298 4919  1963  4919    .    .
 3 19172 2429  1451  2429 -4.6 -3.2
 4  6105 2303  2437  5930   -2 -3.3
 5  2564 2961  6105  2564 -2.9 -3.1
 6  6163 2564  2306  6163 -3.5 -3.2
 7  4039 1975  4857  2115 -2.7 -1.8
 8  5280 7427  4039  5280   -5   -3
 9  3897 5877  2306  5877    .    .
10  1736  591  3086  1736 -5.4 -2.4
11  3086 5078  1736  3086 -5.3 -2.7
12  4625  591  1736   591 -5.7 -2.6
13  4625 1694  5624  1694 -3.8 -2.1
14  1803 4271  2796  4271 -4.5 -2.3
15  6199  298  5097  6199 -4.3 -2.2
16   167 5142  5109   167 -4.4 -1.8
17  5349 5009 15189 15189    .    .
18  1975 1981  2465     .    .    .
19  2465 1981  1975     .    .    .
20  1975 4039  1981     .    .    .
21  1975 4039  1981  1975 -5.3 -2.5
22  1975 1981  4039     .    .    .
23  1981  760  1975  1981 -5.8 -2.4
24  5839 5640  3631  5839 -5.8 -2.6
25  3867 6159  1503  1792 -3.9 -2.3
26  5640 6157  5344  5640 -5.9   -3
27  1503   44   642     .    .    .
28   642   44   691    44 -4.9 -2.1
29  4841 3639   701  1451   -5 -3.3
30   704 4857  5014  4857 -5.7 -2.6
31  3640 3254  1792  3254 -3.9 -2.3
end

reshape long closest_station, i(district) j(which)
frame put station which temp_a22312 temp_a22313, into(temp)
frame temp: contract station temp_a22312 temp_a22313
frlink m:1 closest_station, frame(temp station)
frget tempc1= temp_a22312 tempc2= temp_a22313, from(temp)
bys district: egen meantempc1= mean(tempc1)
bys district: egen meantempc2= mean(tempc2)
bys district (station): replace temp_a22312= meantempc1 if missing(station[1])
bys district (station): replace temp_a22313= meantempc2 if missing(station[1])
drop meantempc* tempc* temp
frame drop temp
reshape wide closest_station, i(district) j(which)
    Res.:

    Code:
    . l, sep(0)

     +---------------------------------------------------------------------------+
     | district   closes~1   closes~2   closes~3   station   te~22312   te~22313 |
     |---------------------------------------------------------------------------|
  1. |        1       1130       4466       1379      1266       -4.9         -4 |
  2. |        2       7298       4919       1963      4919          .          . |
  3. |        3      19172       2429       1451      2429       -4.6       -3.2 |
  4. |        4       6105       2303       2437      5930         -2       -3.3 |
  5. |        5       2564       2961       6105      2564       -2.9       -3.1 |
  6. |        6       6163       2564       2306      6163       -3.5       -3.2 |
  7. |        7       4039       1975       4857      2115       -2.7       -1.8 |
  8. |        8       5280       7427       4039      5280         -5         -3 |
  9. |        9       3897       5877       2306      5877          .          . |
 10. |       10       1736        591       3086      1736       -5.4       -2.4 |
 11. |       11       3086       5078       1736      3086       -5.3       -2.7 |
 12. |       12       4625        591       1736       591       -5.7       -2.6 |
 13. |       13       4625       1694       5624      1694       -3.8       -2.1 |
 14. |       14       1803       4271       2796      4271       -4.5       -2.3 |
 15. |       15       6199        298       5097      6199       -4.3       -2.2 |
 16. |       16        167       5142       5109       167       -4.4       -1.8 |
 17. |       17       5349       5009      15189     15189          .          . |
 18. |       18       1975       1981       2465         .      -5.55      -2.45 |
 19. |       19       2465       1981       1975         .      -5.55      -2.45 |
 20. |       20       1975       4039       1981         .      -5.55      -2.45 |
 21. |       21       1975       4039       1981      1975       -5.3       -2.5 |
 22. |       22       1975       1981       4039         .      -5.55      -2.45 |
 23. |       23       1981        760       1975      1981       -5.8       -2.4 |
 24. |       24       5839       5640       3631      5839       -5.8       -2.6 |
 25. |       25       3867       6159       1503      1792       -3.9       -2.3 |
 26. |       26       5640       6157       5344      5640       -5.9         -3 |
 27. |       27       1503         44        642         .       -4.9       -2.1 |
 28. |       28        642         44        691        44       -4.9       -2.1 |
 29. |       29       4841       3639        701      1451         -5       -3.3 |
 30. |       30        704       4857       5014      4857       -5.7       -2.6 |
 31. |       31       3640       3254       1792      3254       -3.9       -2.3 |
     +---------------------------------------------------------------------------+

    Comment

    • #3
      Dear Mister Musau,
      thanks for your response and your suggestion on how to handle the data. I really appreciate your input. However, I apologize that I do not describe my data explicitly enough. First of all, there are multiple weather stations in some districts. Therefore, they occur twice or even more often in the dataset.The temperature data refers to the variable “station” in the same row and not to the 3 closest stations at once. I did sort the data by district to make this point (hopefully) a little more clear. Some of the stations do not provide temperature data. In case there are multiple stations in a district, this is no issue. I'm primarily interested in the districts where not a single station is located (e.g. districts 18, 19, 20). Here is where I want to use the temperature values of up to the 3 closest stations and caluclate a temperature average.
      Second, I analyze much more than only two dates. I just simplified the table using 22312 and 22313 as example dates. In my analysis, I will cover a time span of over one year. Also, I will not only investigate temperature variables but also plenty of other weather indicators (heat, frost…). Third, I will match the weather data with individual data in a further step. This is why I would prefer to maintain my current data layout.

      If you have any further questions or suggestions, I would be really grateful. Thank you for your help!


      Jessica


      district closest_station1 closest_station2 closest_station3 station temp_a22312 temp_a22313
      1 4466 1379 4896 1379 . .
      1 4466 1379 4896 1666 -3.3 -3.8
      1 4466 1379 4896 1266 -4.9 -4
      1 4466 1379 4896 4466 -3.3 -3.4
      1 4466 1379 4896 2437 -4.2 -4
      1 4466 1379 4896 4896 -2.7 -3.5
      2 7298 4919 1963 4393 -4.8 -3.4
      2 7298 4919 1963 4919 . .
      2 7298 4919 1963 2907 -3.2 -4.5
      2 7298 4919 1963 7298 -3.7 -4.1
      2 7298 4919 1963 1963 . .
      2 7298 4919 1963 3032 -2.6 -2.9
      2 7298 4919 1963 788 . .
      3 19172 2429 1451 19171 -5.7 -3.7
      3 19172 2429 1451 1200 -5.6 -4.4
      3 19172 2429 1451 19172 -4.9 -3.9
      3 19172 2429 1451 2429 -4.6 -3.2
      4 6105 2303 2437 6105 -4.2 -3.8
      4 6105 2303 2437 5930 -2 -3.3
      4 6105 2303 2437 2303 -4.9 -4.6
      4 6105 2303 2437 7427 -5.4 -3.8
      5 2564 2961 6105 2564 -2.9 -3.1
      6 6163 2564 2306 6163 -3.5 -3.2
      6 6163 2564 2306 2306 -3.4 -3
      7 4039 1975 4857 2115 -2.7 -1.8
      7 4039 1975 4857 4039 -5.6 -2.7
      8 5280 7427 4039 5280 -5 -3
      9 3897 5877 2306 3897 -3 -2.4
      9 3897 5877 2306 5516 -2.7 -1.4
      9 3897 5877 2306 5877 . .
      10 1736 591 3086 1736 -5.4 -2.4
      11 3086 5078 1736 3086 -5.3 -2.7
      12 4625 591 1736 591 -5.7 -2.6
      12 4625 591 1736 4625 -4.1 -2.3
      13 4625 1694 2578 2578 -4.5 -2.7
      13 4625 1694 2578 1694 -3.8 -2.1
      13 4625 1694 2578 596 -4.1 -2.7
      13 4625 1694 2578 6101 . .
      13 4625 1694 2578 3196 -4.2 -2.2
      14 1803 4271 2796 1803 -5.6 -2.7
      14 1803 4271 2796 4271 -4.5 -2.3
      15 6199 298 5097 183 -1.5 -1.8
      15 6199 298 5097 2201 -2.1 -1.2
      15 6199 298 5097 5097 -5.6 -2.1
      15 6199 298 5097 6199 -4.3 -2.2
      15 6199 298 5097 4024 -3.1 -2.2
      15 6199 298 5097 1757 -3.8 -2
      15 6199 298 5097 6097 . .
      15 6199 298 5097 298 -5.4 -2.6
      16 167 5142 5109 7351 -4.5 -1.5
      16 167 5142 5109 167 -4.4 -1.8
      16 167 5142 5109 1759 . .
      16 167 5142 5109 5142 -3.8 -1.7
      16 167 5142 5109 6109 -4.3 -1.4
      16 167 5142 5109 6310 -4.3 -2.3
      16 167 5142 5109 5109 -4.2 -1.6
      17 5349 5009 15189 2796 -5.8 -2.6
      17 5349 5009 15189 15189 . .
      17 5349 5009 15189 5349 -3 -1.6
      17 5349 5009 15189 5009 -4.6 -2.1
      17 5349 5009 15189 6106 . .
      18 1975 1981 4039 . . .
      19 1981 1975 4857 . . .
      20 1975 4039 1981 . . .




      Code:
      egen group_district = group(district) //districts with station but without data
egen has_missing_tmk = max(missing(temp_a22312 - temp_a22313)), by(group_district) // Identify districts with stations having missing values on tmk* variables
egen has_data_tmk = max(temp_a22312 - temp_a22313 != .), by(group_district) // Identify districts with at least one station having data on tmk* variables
gen districts_to_check = has_missing_tmk & !has_data_tmk & station !=. //Identify districts that meet the criteria
list district if districts_to_check

sort district station

levelsof district, local(district_list)
loca date_list 22312 22313

foreach district in `district_list' {
    gen closest_station1_`district' = closest_station1 if district == `district'
    gen closest_station2_`district' = closest_station2 if district == `district'
    gen closest_station3_`district' = closest_station3 if district == `district'

    foreach date in `date_list' {
        egen temp_avg`district'`date' = mean(temp_a`date') if station == closest_station1_`district' | station == closest_station2_`district' | station == closest_station3_`district'
       replace temp_a`date' = temp_avg`district'`date' if (missing(temp_a`date')) & (station == . | districts_to_check == 1)
    }
}

      Comment

      • #4
        Can you fill in the averages that you expect for the 3 stations 18, 19, 20?

        18 1975 1981 4039 . . .
        19 1981 1975 4857 . . .
        20 1975 4039 1981 . . .
        Fill in the dots from your manual calculations. This will be clearer than trying to explain what is wanted.

        Comment

        • #5
          Yes, of course. The closest three stations to district 18 are 1975, 1981 and 4039. For station 4039 tempa_22312 has a value of -5.6 (row 27), 1981 has a value of -2.7 (row 67, not displayed in the table above) and for station 1975 there is no temp value. So the mean of temp_a22312 would be -5.5 for district 18 and district 20 (since the 3 closest stations are the same). For district 19:Station 1981 has a value of -5.8, 1975 has no value and station 4857 has a temp value of -5.7. So the temp_a22312 mean for district 19 is -5,75

          For temp_a2213 and district 18 (20), we have a value of -2.7 for station 4039 (row 27), 1981 has a value of -2.4 (row 67, not displayed in the table above) and for station 1975 there is no temp value again. The mean temp_a22313 would be -2.55 for district 18 and 20. The colum for station stays missing, since there are no stations directly kocated in these three districts.

          district closest_station1 closest_station2 closest_station3 station temp_a22312 temp_a22313
          18 1975 1981 4039 . -5.5 -2.55
          19 1981 1975 4857 -5.75 -2.50
          20 1975 4039 1981 . -5.5 -2.55

          Comment

          • #6
            981 has a value of -2.7 (row 67, not displayed in the table above)
            Do not use values from outside the dataset presented. I am struggling to see how the code in #2 does not give you what you want save for changing the identifiers and generalizing to several temperature variables. Below, I make the assumption that all such temperature variables have the prefix "temp_a". Again, make comments only in relation to the dataset presented, not to some observations not appearing here.

            Code:
            * Example generated by -dataex-. To install: ssc install dataex
clear
input byte district int(closest_station1 closest_station2 closest_station3 station) float(temp_a22312 temp_a22313)
 1  4466 1379  4896  1379    .    .
 1  4466 1379  4896  1666 -3.3 -3.8
 1  4466 1379  4896  1266 -4.9   -4
 1  4466 1379  4896  4466 -3.3 -3.4
 1  4466 1379  4896  2437 -4.2   -4
 1  4466 1379  4896  4896 -2.7 -3.5
 2  7298 4919  1963  4393 -4.8 -3.4
 2  7298 4919  1963  4919    .    .
 2  7298 4919  1963  2907 -3.2 -4.5
 2  7298 4919  1963  7298 -3.7 -4.1
 2  7298 4919  1963  1963    .    .
 2  7298 4919  1963  3032 -2.6 -2.9
 2  7298 4919  1963   788    .    .
 3 19172 2429  1451 19171 -5.7 -3.7
 3 19172 2429  1451  1200 -5.6 -4.4
 3 19172 2429  1451 19172 -4.9 -3.9
 3 19172 2429  1451  2429 -4.6 -3.2
 4  6105 2303  2437  6105 -4.2 -3.8
 4  6105 2303  2437  5930   -2 -3.3
 4  6105 2303  2437  2303 -4.9 -4.6
 4  6105 2303  2437  7427 -5.4 -3.8
 5  2564 2961  6105  2564 -2.9 -3.1
 6  6163 2564  2306  6163 -3.5 -3.2
 6  6163 2564  2306  2306 -3.4   -3
 7  4039 1975  4857  2115 -2.7 -1.8
 7  4039 1975  4857  4039 -5.6 -2.7
 8  5280 7427  4039  5280   -5   -3
 9  3897 5877  2306  3897   -3 -2.4
 9  3897 5877  2306  5516 -2.7 -1.4
 9  3897 5877  2306  5877    .    .
10  1736  591  3086  1736 -5.4 -2.4
11  3086 5078  1736  3086 -5.3 -2.7
12  4625  591  1736   591 -5.7 -2.6
12  4625  591  1736  4625 -4.1 -2.3
13  4625 1694  2578  2578 -4.5 -2.7
13  4625 1694  2578  1694 -3.8 -2.1
13  4625 1694  2578   596 -4.1 -2.7
13  4625 1694  2578  6101    .    .
13  4625 1694  2578  3196 -4.2 -2.2
14  1803 4271  2796  1803 -5.6 -2.7
14  1803 4271  2796  4271 -4.5 -2.3
15  6199  298  5097   183 -1.5 -1.8
15  6199  298  5097  2201 -2.1 -1.2
15  6199  298  5097  5097 -5.6 -2.1
15  6199  298  5097  6199 -4.3 -2.2
15  6199  298  5097  4024 -3.1 -2.2
15  6199  298  5097  1757 -3.8   -2
15  6199  298  5097  6097    .    .
15  6199  298  5097   298 -5.4 -2.6
16   167 5142  5109  7351 -4.5 -1.5
16   167 5142  5109   167 -4.4 -1.8
16   167 5142  5109  1759    .    .
16   167 5142  5109  5142 -3.8 -1.7
16   167 5142  5109  6109 -4.3 -1.4
16   167 5142  5109  6310 -4.3 -2.3
16   167 5142  5109  5109 -4.2 -1.6
17  5349 5009 15189  2796 -5.8 -2.6
17  5349 5009 15189 15189    .    .
17  5349 5009 15189  5349   -3 -1.6
17  5349 5009 15189  5009 -4.6 -2.1
17  5349 5009 15189  6106    .    .
18  1975 1981  4039     .    .    .
19  1981 1975  4857     .    .    .
20  1975 4039  1981     .    .    .
end

gen id= cond(!missing(station), station, -_n)
reshape long closest_station, i(id) j(which)
frame put station which temp_a*, into(temp)
frame temp: contract station temp_a*
frlink m:1 closest_station, frame(temp station)
qui ds temp_a*
local list
forval i= 1/`=wordcount("`r(varlist)'")'{
    local list `list' tempc`i'= `=word("`r(varlist)'", `i')' 
}
frget `list', from(temp)
qui ds temp_a*
forval i= 1/`=wordcount("`r(varlist)'")'{
    bys district: egen meantempc`i'= mean(tempc`i')
    qui ds temp_a*
    bys district (station): replace `=word("`r(varlist)'", `i')'= meantempc`i' if missing(station[1])
}
drop meantempc* tempc* temp
frame drop temp
reshape wide closest_station, i(id) j(which)
            Res.:

            Code:
            . sort station

. l, sep(0)

     +-----------------------------------------------------------------------------------+
     |    id   closes~1   closes~2   closes~3   district   station   te~22312   te~22313 |
     |-----------------------------------------------------------------------------------|
  1. |   167        167       5142       5109         16       167       -4.4       -1.8 |
  2. |   183       6199        298       5097         15       183       -1.5       -1.8 |
  3. |   298       6199        298       5097         15       298       -5.4       -2.6 |
  4. |   591       4625        591       1736         12       591       -5.7       -2.6 |
  5. |   596       4625       1694       2578         13       596       -4.1       -2.7 |
  6. |   788       7298       4919       1963          2       788          .          . |
  7. |  1200      19172       2429       1451          3      1200       -5.6       -4.4 |
  8. |  1266       4466       1379       4896          1      1266       -4.9         -4 |
  9. |  1379       4466       1379       4896          1      1379          .          . |
 10. |  1666       4466       1379       4896          1      1666       -3.3       -3.8 |
 11. |  1694       4625       1694       2578         13      1694       -3.8       -2.1 |
 12. |  1736       1736        591       3086         10      1736       -5.4       -2.4 |
 13. |  1757       6199        298       5097         15      1757       -3.8         -2 |
 14. |  1759        167       5142       5109         16      1759          .          . |
 15. |  1803       1803       4271       2796         14      1803       -5.6       -2.7 |
 16. |  1963       7298       4919       1963          2      1963          .          . |
 17. |  2115       4039       1975       4857          7      2115       -2.7       -1.8 |
 18. |  2201       6199        298       5097         15      2201       -2.1       -1.2 |
 19. |  2303       6105       2303       2437          4      2303       -4.9       -4.6 |
 20. |  2306       6163       2564       2306          6      2306       -3.4         -3 |
 21. |  2429      19172       2429       1451          3      2429       -4.6       -3.2 |
 22. |  2437       4466       1379       4896          1      2437       -4.2         -4 |
 23. |  2564       2564       2961       6105          5      2564       -2.9       -3.1 |
 24. |  2578       4625       1694       2578         13      2578       -4.5       -2.7 |
 25. |  2796       5349       5009      15189         17      2796       -5.8       -2.6 |
 26. |  2907       7298       4919       1963          2      2907       -3.2       -4.5 |
 27. |  3032       7298       4919       1963          2      3032       -2.6       -2.9 |
 28. |  3086       3086       5078       1736         11      3086       -5.3       -2.7 |
 29. |  3196       4625       1694       2578         13      3196       -4.2       -2.2 |
 30. |  3897       3897       5877       2306          9      3897         -3       -2.4 |
 31. |  4024       6199        298       5097         15      4024       -3.1       -2.2 |
 32. |  4039       4039       1975       4857          7      4039       -5.6       -2.7 |
 33. |  4271       1803       4271       2796         14      4271       -4.5       -2.3 |
 34. |  4393       7298       4919       1963          2      4393       -4.8       -3.4 |
 35. |  4466       4466       1379       4896          1      4466       -3.3       -3.4 |
 36. |  4625       4625        591       1736         12      4625       -4.1       -2.3 |
 37. |  4896       4466       1379       4896          1      4896       -2.7       -3.5 |
 38. |  4919       7298       4919       1963          2      4919          .          . |
 39. |  5009       5349       5009      15189         17      5009       -4.6       -2.1 |
 40. |  5097       6199        298       5097         15      5097       -5.6       -2.1 |
 41. |  5109        167       5142       5109         16      5109       -4.2       -1.6 |
 42. |  5142        167       5142       5109         16      5142       -3.8       -1.7 |
 43. |  5280       5280       7427       4039          8      5280         -5         -3 |
 44. |  5349       5349       5009      15189         17      5349         -3       -1.6 |
 45. |  5516       3897       5877       2306          9      5516       -2.7       -1.4 |
 46. |  5877       3897       5877       2306          9      5877          .          . |
 47. |  5930       6105       2303       2437          4      5930         -2       -3.3 |
 48. |  6097       6199        298       5097         15      6097          .          . |
 49. |  6101       4625       1694       2578         13      6101          .          . |
 50. |  6105       6105       2303       2437          4      6105       -4.2       -3.8 |
 51. |  6106       5349       5009      15189         17      6106          .          . |
 52. |  6109        167       5142       5109         16      6109       -4.3       -1.4 |
 53. |  6163       6163       2564       2306          6      6163       -3.5       -3.2 |
 54. |  6199       6199        298       5097         15      6199       -4.3       -2.2 |
 55. |  6310        167       5142       5109         16      6310       -4.3       -2.3 |
 56. |  7298       7298       4919       1963          2      7298       -3.7       -4.1 |
 57. |  7351        167       5142       5109         16      7351       -4.5       -1.5 |
 58. |  7427       6105       2303       2437          4      7427       -5.4       -3.8 |
 59. | 15189       5349       5009      15189         17     15189          .          . |
 60. | 19171      19172       2429       1451          3     19171       -5.7       -3.7 |
 61. | 19172      19172       2429       1451          3     19172       -4.9       -3.9 |
 62. |   -63       1981       1975       4857         19         .          .          . |
 63. |   -64       1975       4039       1981         20         .       -5.6       -2.7 |
 64. |   -62       1975       1981       4039         18         .       -5.6       -2.7 |
     +-----------------------------------------------------------------------------------+

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