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MindMap Gallery ANALYSE information
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ANALYSE information
This is a mind map about data analysis, including quick calculation, staring method, Theoretical basis, theory, etc. Friends in need hurry up and collect it!
Edited at 2024-02-08 12:01:39
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ANALYSE information
- Zootopia 2 Easter Egg
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
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- Outline
ANALYSE information
Speed calculation
High stack
Applicable to addition operation
Start adding from the highest position. If you want to add if the layers are misaligned, try to do the math orally.
Start adding from the highest position. If you want to add if the layers are misaligned, try to do the math orally.
mantissa method
The accuracy of the options is consistent with the material, and the options have different mantissas. Sometimes you can look at the last two digits.
Calculate the mantissa of each data and combine it with options to kill instantly
division
peak shaving and valley filling
Add multiple numbers and average
① Polyline or columnar data - combine the options to draw a baseline and see if the peaks and valleys can be offset exactly ②Pure digital materials - select the benchmark, find peaks and valleys, peak-shaving and valley-filling - average = benchmark value + average after peak-shaving and valley-filling
underline subtraction
multi-digit subtraction
① There is a critical value - draw a line based on the critical value, make a difference between the two numbers and the critical value, and add the differences to get the result ② No critical value - "12" or "21" underline, try to ensure that there is no borrowing, and the mouth will be counted as a difference
Turn multiplication into addition
Quick multiplication
Quick calculation of multiplication of any two-digit number - front and back, inside and outside
Special numbers:
A number × 1.5 is equal to itself + half of itself
A number × 1.1 is equal to this number and you want to add it
A number × 0.9 is equal to the misalignment of this number.
truncation
General tips for division
Look ahead option If large, cut off two digits If small, cut to three digits One-step denominator Cut off multiple steps
Magnitude: consider decimal point, percent sign, unit
How to cut: Just keep the first few digits and round up the next digit.
Who to cut off: one-step division, only cut off the denominator Multi-step division, truncate both numerator and denominator (reduction after truncation)
Cut off a few numbers: (Look at the gap between options: find the gap between the closest options)
1. The options are very different (cut off by two digits). The first positions are all different. The first positions are the same. The difference between the second positions is > the first position.
2. The difference between the options is small (cut off to three digits). The first place is the same, and the difference between the second place ≤ the first place.
100%
Quick calculation skills for multiplication and division
If a percentage in the calculation formula can be directly converted or approximately converted into a common fraction Under normal circumstances, it is converted into the form of 1/n, and then the operation is performed
There is a big gap between the options, it’s about 100 percent.
The gap between the options is small and must be an accurate percentage.
100% speed calculator
1/2=50% 1/4=25% 1/8=12.5% 1/16=6.25%
1/5=20% 1/10=10% 1/20=5%
1/13=7.7% 1/15=6.7%
1/3=33.3% 1/6=16.7% 1/12=8.3%
1/7=14.3% 1/14=7.1% 1/9=11.1% 1/11=9.1%
1/17=5.9% 1/18=5.6% 1/19=5.3%
Split method
Quick calculation skills for multiplication and division
Core: option, first split out the special percentage, and the remaining number is how many times a point in the denominator is
Division: By breaking a molecule into its parts, Calculate separately and obtain corresponding results through step-by-step decomposition
If the numerator is close to the denominator, you can subtract it by 1
If the numerator is greater than 50%, split 50% first
If the numerator is less than 50%, it can be reduced by 50%
Multiplication: If a multiplier is a percentage and can be split into two simple values, we split the percentage into two parts and multiply them
135%=1 0.35
Misalignment correction (same scaling)
Principle: The numerator and denominator of a fraction are added and subtracted by the same multiple at the same time, and the size of the fraction remains unchanged.
Speed calculation
The numerator and denominator take the first three significant figures respectively.
Stagger the same bits, add and subtract the same times (the multiples should be as small as possible)
The smaller correction number = b × 1% of the original number
The larger correction number = a × 1/10 of the original number × 1% of the original number
Get results quickly
Score comparison
One big and one small: the one with the bigger molecule has the bigger score (more money, more people, less money)
Tongdatong small:
Directly divide vertically, compare quotient
Comparing multiples horizontally, whoever has a higher multiple will listen to whoever has it
The greater the multiple of the molecule, the greater the fraction
The denominator is a multiple that is large and the fraction is small
special number
stare
ratio size
If possible, eliminate first, then compare.
None of the four can be ruled out, except vertically.
Stare Dafa
There is a big gap in options, who will you love?
Comparison of two periods
a>b,↑ a<b,↓
Formulas
Base period ratio: more people have less money
Comparison of growth volume: if it is large, it will be large. If it is large or small, it depends on the multiple.
Mixed growth rate: mixed in the middle, with large bias
Examiner's thinking
base period sum difference
Current pit
How many times more = how many times - 1
interpolation method
Special score, verification
Squares
average annual growth rate
Theoretical basis
Material reading
written material
structural reading method
lap time
main body of painting
Key words
physical structure
form material
Heavy header
Sweep vertically
Note traps: unit, magnitude, accumulation (time)
graphic material
Look at the title
to the legend
Note special
Classification
pie chart
Arrange clockwise along the 12 o'clock direction, in order
Comprehensive materials
Look separately
Pay attention to the connections between different types of materials
theory
Base period volume
calculate
Base period = current period – growth amount
mantissa method, estimate, stare
Base period = current period/1 r
|r|＞5% truncated division, percentile (be sure to pay attention to the options)
|r|≤5%, turn division into multiplication, stare (division into multiplication, subtraction into addition or addition into subtraction)
There is a big gap between the options, and it’s an approximate estimate. The gap between options is small, and the score needs to be accurate The difference between options is very small, no cents required
267/128 direct removal or correction The gap between options is small: straight division and truncation to three digits Correction needs to be precise
Compare
two steps
Let’s rule it out first. Those with more money and less money belong to the big ones. Compare again, fractions are larger than
Different subjects
Let’s rule it out with a glare first. There are many people with little money. |r|≤10%, when the gap between the current period and the current period is large, it is directly compared with the current period The current gap is very close and needs to be eliminated directly
The options are different, use the elimination method to directly stare at
What's the ranking?
First stare at the first place and eliminate the magnitude If necessary, list the formula (need to compare)
base period sum difference
formula
(A/1+a)±(B/1 b)
First look at the current pitfalls (A±B) and exclude them Look at the plus and minus again and rule out ①If all the exclusions are completed, it will be a flash sale. ②If r is 100% better, the growth can be calculated (A-B)-(△A-△B) ③If the difference between the options is small and r is not special, divide or correct (the denominators are the same)
Base period difference≈A-B/1 a
If A is much larger than B, just make a bold estimate: base period difference ≈ A-B/1 a
Surplus = Exports – Imports
Let’s first look at the current pitfalls Analyze and stare
January-February = first quarter-March
Let’s first look at the current pitfalls Analyze and stare
Shun: out＞in, reverse: out＜in
Let’s first look at the current pitfalls Look at the positive and negative again
Difference=June-January
First look at the current pitfalls, and then analyze them in detail or take advantage of growth Base period difference = (A-B)-(△A-△B)
January-June=January-July-July
Let’s first look at the current pitfalls Then mix thoughts and stare
Current volume
formula
Current period = base period + growth amount
mantissa method, estimate, stare
Current period = base period × (1 r)
special number Turn multiplication into addition
Catch-up question type Keep the increment or growth rate unchanged Ask in which year a specific amount was exceeded
Current period = base period + n × growth amount Keep the increment unchanged If it is exceeded for the first time, convert the units first and then calculate
substitution method, estimation
Current period = Base period × (1 r) Growth rate is unknown
Estimated based on growth (smaller than actual value) 2.47×2.47/2.28 geometric sequence
The growth rate is the same from 2015-2017-2019
①2019=2017×2017/2015 ②Estimated based on increments (smaller than actual value)
Current period = base period × (1 r)² Keep growth rate unchanged substitution method, square numbers
①Perfect square
Substitute option verification
②Interval current period
Current period = base period × (1 r period)
Base period current special type
Given the growth amount and r, find the base period and current period Formula: base period = growth/r (glare)
If you ask about the current period, pay attention to the traps Current period=base period growth amount
Given the current period calculated based on the nominal growth rate, find the current period value calculated based on the actual growth rate. Formula: Actual current period = (nominal current period/1 r nominal) x (1 r actual)
The actual current period is slightly smaller than the nominal current period (direct glare)
general growth rate
calculate
Percentage and percentage point high minus low plus
Given the growth rate, find the multiple - how many times is it = growth rate 1
Number: How many percent is it? Double: n times = 2ⁿ times
Growth rate: Ratio with sign
Decline: compare absolute values
① Without sign "high minus low plus" ②Restore: negative sign
Range of change: compare absolute values
Calculation formula
Known percentages and percentage points: high minus low plus (direct glare)
The specific amount is known: r = growth amount / current period - growth amount = (current period - base period) ÷ base period = current period / base period - 1 Growth amount/base period
Stare, truncate and divide, 100%
First add the base period and current period, and then calculate the growth rate
Cut to two digits
Special test method: class growth rate A is more or less than B? %
Set of formulas: r=(A-B)÷B
How many have r>10%?
Current period - base period > 0.1 base period Current period>1.1 base period
r＞15%——Current period＞1.1 base period+0.05 base period (the decimal point moves half of one place to the left)
r＞20%——Current period＞Base period+0.2 base period (twice the decimal point moved one place to the left)
r＞2%——Current period＞Base period+0.02 base period (twice the decimal point moved two places to the left)
r>50%——Current period>1.5 base period (base period + half of the base period)
comparison class
The fastest (slowest) growth/decline is
Known current period, base period, comparison r
①Current period/base period (note the magic use of special numbers) 1.1 base period
②If you can’t stare, compare the growth amount/base period
The height difference between the pillars is almost the same, just stare, the base period is small, r is large
①Online=retail terminal-physical (underline subtraction first) ②Re-staring period/base period (special number 1.5)
Known current period, growth amount, comparison r
Stare at the growth amount/current period. If you can stare out, you will be instantly killed.
Line chart problem
Elimination method: look at the best value, look at the trend, and make comparisons
Sorting problems
①Start at the current period/base period first, if you can’t stare at it ②Compare the growth amount/base period (underlined subtraction)
special growth rate
interval growth rate
There is one year between the two times. If the growth rate is known, find the growth rate.
Formula: r1＋r2＋r1×r2
When the absolute values of r1 and r2 are <10%, only the sum is calculated and the product can be ignored. Otherwise, a rough estimate can be made Soul: Combining Options to Stare Answers
Inverse operation of interval growth rate (double base period r)
Given r and r1, find r2 r2＝r-r1/1＋r1
Interval multiple (known growth rate)
Calculate the interval r first (the product is ignored) Interval multiple = r space + 1
Interval base period amount
Base period = current period/1+r period
Average annual growth rate comparison
Time period + annual average..., highest/lowest growth rate (sorting)
Formula: (1 r)ⁿ=current amount/base period amount (n is the year difference between the current period and the base period)
Directly stare at the current period volume/base period volume Stare at the first person
Average annual growth rate calculation
Formula: (1 r)ⁿ=current amount/base period amount (n is the year difference between the current period and the base period)
Calculation: When |r|≤10%, then (1+r)ⁿ≈1+nr When |r|＞10%, then (1＋r)ⁿ＞1+nr, combined with substitution verification (centered substitution)
Quick calculation tool: square numbers 11²=121 12²=144 13²=169 14²=196 15²=225 16²=256 17²=289 18²=324 19²=361
Quick calculation tool: Power numbers 1.2³=1.7 1.2⁴=2.0 1.1⁵=.161 1.3³=2.2 1.3⁴=2.9 1.4³=2.7 1.4⁴=3.8
mixed growth rate
Subject mix: export + import = import and export Time mix: January-February + March = 1 quarter
Mix the main body and find the parts (subtractive transformation) Surplus + Expenditure = Revenue
Mix the main bodies and find the total amount (distance and amount are inversely proportional) Import + Export = Import and Export
Time mixing, find the part (large bias vector) January-February + March = January-March
Surplus = Exports – Imports Exports = Imports + Surplus
Method One: Three Carrots and Three Pitfalls The center is not centered after mixing (minimum growth rate < total growth rate < maximum growth rate) Prefer those with large base period volume
Method 2: Line segment method calculation Tip: Write both sides before mixing, write the middle after mixing, distance is inversely proportional to quantity (essentially, quantity is the denominator)
Mixed growth rate inverse operation
The growth rate of each entity is known, and the base period proportional relationship of the quantity (proportion, multiple) First find the mixed relationship: A=B C Using the line segment method again, distance and quantity are inversely proportional
Mixed growth rate extension①
Given the cumulative growth rate, determine the relationship between the current month and the cumulative growth rate. There is a broken line - as long as the mind does not slip, the current month will always be more than the cumulative amount
Mixed growth rate extension②
Known proportions (specific gravity, average), find the proportional relationship of specific quantities First find the mixed relationship: A=B C Using the line segment method again, the distance (between the proportions) and the amount (the denominator of the proportion) are inversely proportional
Given the average, find the multiple of the quantity (there is a mixed relationship) Urban + rural area = whole country distance is inversely proportional to quantity
Given the average, find the ratio of the quantities (there is a mixed relationship) Urban + rural area = whole country distance is inversely proportional to quantity
Given the specific gravity, find the specific gravity of the quantity (there is a mixed relationship) Import + Export = Import and Export Mixed center, large bias
product growth rate
The core is a product relationship, find the growth rate Three-quantity relationship: A=B×C Features of the question: Given the growth rate b of B and the growth rate c of C, find the growth rate a of A. a=b c b×c（r1＋r2＋r1×r2）
Transaction volume = area × average price a＝b＋c＋b×c
Increment
Computing
Growth + unit (specific amount) Test method ①: The current period and base period are known: Growth amount = current period - base period (glare, underline subtraction) Special: average annual growth = current period - base period/year difference (the selection of the base period is consistent with the average annual growth rate) Test method ②: The current period and r are known: 100 percent growth = base period × r = current period / (1 + r) × r The first step: centigrade, |r|=1/n Step 2: Growth amount = current period/n+1 Decrease = current period/n-1
Average annual growth (ordinary years) Current period - base period/n
Average annual growth (five-year plan) Current period - base period/n (base period is pushed forward one year)
Given the current period, r, find the increment r＝5.26≈1/19 Growth amount = current period/n+1
Given the current period, r, find the increment |r|＝19.6%≈1/5 Decrease current period/n-1
Given the current period, r, find the increment r＝4.2% is smaller (<5%) The growth amount is slightly less than the current period × r
Given the current period, r, find the increment r＝87% is larger (>50%) formula glare Current period/(1+r)×r
Given the current period, r, find the increment exceeding a certain number Growth amount > 120 (popular test method) Give priority to choosing the right one, neither too big nor too small. Combined with comparing stares and counting ticks
Given the current period, r, find the increment r＝4.2% is smaller (<5%) The growth amount is slightly less than the current period × r
Given the current period, r, find the increment r＝87% is larger (>50%) formula glare Current period/(1+r)×r
Given the current period, r, find the increment exceeding a certain number Growth amount > 120 (popular test method) Give priority to choosing the right one, neither too big nor too small. Combined with comparing stares and counting ticks
Given the increment of A, find the increment of non-A Non-A growth = overall increase – A increase
100% speed calculator
1/2=50% 1/4=25% 1/8=12.5% 1/16=6.25%
1/5=20% 1/10=10% 1/20=5%
1/13=7.7% 1/15=6.7%
1/3=33.3% 1/6=16.7% 1/12=8.3%
1/7=14.3% 1/14=7.1% 1/9=11.1% 1/11=9.1%
1/17=5.9% 1/18=5.6% 1/19=5.3%
scaling method
1.43% uses 14.3=1/7, and the denominator moves forward one place 22% utilizes 11% = 1/9, multiply the numerator by 2
Find the middle method
14.3%＜15.4%＜16.7%, between 1/7 and 1/6, take 1/6.5 16.7%＜18.5%＜20%, between 1/6 and 1/5, take 1/5.5
direct division
n=100/the number before the percent sign 44%＝1/100/44（n＝100/44）
comparison class
Growth + most or least (sort) Test method ① The current period and base period are known: Growth amount = current period - base period (glare, underline division) Column chart, line chart, directly see the height difference
Test method ② Known current period sum r: hundred percent Growth amount=base period×r=current period/(1+r)×r The formula: if it is big, it will be big - if the current period is big and the growth rate is big, the growth will be big. If the current period is large and the decline is large, the reduction will be large (note the negative number) One large and one hundred cents (multiples) Draw an arrow and listen to whoever gets the bigger multiple.
Pay attention to negative numbers
The current period is very small, r is very large, and the growth is not necessarily large.
There are positive and negative, big is big, big and small are divided into hundreds. ①The positive ratio is positive, the negative ratio is negative ②One positive and one negative cent percent Growth amount = current period/n+1 Decrease = current period/n-1