How the landläufigkeit.index is made
The index turns 27 measures into one number from 0 to 100. We work it out step by step, with Köln as the example.
Step 1 of 4
1. Each figure becomes points
Euros, minutes and percentages cannot be added up. So only a district's place among all 400 counts. We show it with one measure: the unemployment rate.
How it is worked out: on the left in general, on the right for Köln.
PP: the points, from 0 (the worst district) to 100 (the best). = uu: the districts with a worse figure. For unemployment: those with a higher rate. + (gg: the districts with exactly the same figure, the district itself counted. Those level count half as worse: (g − 1) ÷ 2. − 1) ÷ 2nn: all districts with a figure, mostly 400. n − 1: all the others but the district itself. − 1 × 100× 100: the share (from 0 to 1) becomes points (from 0 to 100).
PKöln does better than 37.5 of the 399 other districts: 9.4 points. = 3737 districts have a higher unemployment rate than Köln (9.0 %): they do worse. + (22 districts have exactly 9.0 %, Köln included. The 1 others count half: (2 − 1) ÷ 2 = 0.5. − 1) ÷ 2400400 districts have a figure; besides Köln, 399. − 1 × 100× 100: the share (from 0 to 1) becomes points (from 0 to 100). = 9.4Köln does better than 37.5 of the 399 other districts: 9.4 points.
Step 2 of 4
2. The points become themes
The 27 measures belong to seven themes. A theme gets the average of its measures' points: add them all up, then divide by how many there are.
T = P1 + P2 + … + Pkk
P: a measure's points · k: the theme's measures with a figure- Work & income(9.4 + 59.1 + 15.3 + 56.0 + 52.4) ÷ 5 = 38.4
- Social & safety(5.5 + 72.1 + 1.5 + 41.4) ÷ 4 = 30.1
- Housing(2.3 + 58.8 + 4.3) ÷ 3 = 21.8
- Health(96.7 + 90.5 + 47.4) ÷ 3 = 78.2
- Everyday life(95.9 + 97.0 + 87.6 + 79.8 + 83.2) ÷ 5 = 88.7
- Nature & climate(25.4 + 29.9 + 65.3 + 94.5) ÷ 4 = 53.8
- Future(91.5 + 8.8 + 18.3) ÷ 3 = 39.5
All 27 measures of Köln
| Measure | Figure | Better | Points |
|---|---|---|---|
| Work & income | |||
| Unemployment rate | 9.0 % | less | 9.4 |
| Disposable income | 28,764 € per person | more | 59.1 |
| Company insolvencies | 47.0 per 10,000 firms | less | 15.3 |
| Electricity use of industry | 2.0 MWh per person | more | 56.0 |
| Long commutes (50 km+) | 11.3 % | less | 52.4 |
| Social & safety | |||
| Child poverty (SGB II) | 21.9 % | less | 5.5 |
| School leavers without qualification | 5.8 % | less | 72.1 |
| Recorded crime | 11,286 per 100,000 | less | 1.5 |
| Youth unemployment (15–24) | 6.0 % | less | 41.4 |
| Housing | |||
| Rent against income | 27.4 % of income | less | 2.3 |
| Homes in new buildings | 3.2 per 1,000 | more | 58.8 |
| Single-person households | 53.6 % | less | 4.3 |
| Health | |||
| Drive time to the nearest GP | 1.9 minutes | less | 96.7 |
| Drive time to the nearest emergency department | 7.2 minutes | less | 90.5 |
| General practitioners | 66 per 100,000 | more | 47.4 |
| Everyday life | |||
| Drive time to the nearest supermarket | 2.3 minutes | less | 95.9 |
| Drive time to the nearest primary school | 2.7 minutes | less | 97.0 |
| Public transport nearby | 99.5 % | more | 87.6 |
| Gigabit internet | 90.7 % | more | 79.8 |
| Drive time to the nearest IC/ICE station | 8.7 minutes | less | 83.2 |
| Nature & climate | |||
| Forest share | 18.0 % | more | 25.4 |
| Hot days | 15.9 days a year | less | 29.9 |
| Days with 20 mm of rain or more | 3.8 days a year | less | 65.3 |
| Land take for settlement & transport | -0.5 m² per person a year | less | 94.5 |
| Future | |||
| Births minus deaths | -1.2 per 1,000 | more | 91.5 |
| Net migration | 4.0 per 1,000 | more | 8.8 |
| Debt of the Land and its municipalities | 11,235 € per person | less | 18.3 |
Step 3 of 4
3. The themes become the index
The index is the average of the seven themes, worked out the same way. Each theme counts the same.
I = T1 + T2 + … + T77
T: a theme's pointsKöln: I = (38.4 + 30.1 + 21.8 + 78.2 + 88.7 + 53.8 + 39.5) ÷ 7 = 50.1
Step 4 of 4
4. The districts become the states
A state is the average of its districts, weighted by their residents: a large district counts more than a small one.
L = E1I1 + E2I2 + … + EmImE1 + E2 + … + Em
E: a district's residents · I: its index · m: districts in the stateNorth Rhine-Westphalia: 53 districts with 18,017,520 residents; Köln counts for 5.7%. The state's index: 46.7, rank 9 of 16.
What the index does not say (the measures' years, crimes where they happen and more): Data & methods →