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I've been trying to calculate median but still I've got some mathematical issues I guess as I couldn't get the correct median value and couldn't figure out why. Here's the code;

class StatsCollector {

    constructor() {
        this.inputNumber = 0;
        this.average = 0;

        this.timeout = 19000;

        this.frequencies = new Map();
        for (let i of Array(this.timeout).keys()) {
            this.frequencies.set(i, 0);
        }
    }

    pushValue(responseTimeMs) {
        let req = responseTimeMs;
        if (req > this.timeout) {
            req = this.timeout;
        }

        this.average = (this.average * this.inputNumber + req) / (this.inputNumber + 1);

        console.log(responseTimeMs / 1000)
        let groupIndex = Math.floor(responseTimeMs / 1000);
        this.frequencies.set(groupIndex, this.frequencies.get(groupIndex) + 1);

        this.inputNumber += 1;
    }

    getMedian() {
        let medianElement = 0;
        if (this.inputNumber <= 0) {
            return 0;
        }
        if (this.inputNumber == 1) {
            return this.average
        }
        if (this.inputNumber == 2) {
            return this.average
        }
        if (this.inputNumber > 2) {
            medianElement = this.inputNumber / 2;
        }

        let minCumulativeFreq = 0;
        let maxCumulativeFreq = 0;
        let cumulativeFreq = 0;
        let freqGroup = 0;
        for (let i of Array(20).keys()) {
            if (medianElement <= cumulativeFreq + this.frequencies.get(i)) {
                minCumulativeFreq = cumulativeFreq;
                maxCumulativeFreq = cumulativeFreq + this.frequencies.get(i);
                freqGroup = i;
                break;
            }
            cumulativeFreq += this.frequencies.get(i);
        }

        return (((medianElement - minCumulativeFreq) / (maxCumulativeFreq - minCumulativeFreq)) + (freqGroup)) * 1000;
    }

    getAverage() {
        return this.average;
    }

}

Here's the snapshot of the results when I enter the values of

342,654,987,1093,2234,6243,7087,20123

The correct result should be;

Median: 1663.5

I've been trying to calculate median but still I've got some mathematical issues I guess as I couldn't get the correct median value and couldn't figure out why. Here's the code;

class StatsCollector {

    constructor() {
        this.inputNumber = 0;
        this.average = 0;

        this.timeout = 19000;

        this.frequencies = new Map();
        for (let i of Array(this.timeout).keys()) {
            this.frequencies.set(i, 0);
        }
    }

    pushValue(responseTimeMs) {
        let req = responseTimeMs;
        if (req > this.timeout) {
            req = this.timeout;
        }

        this.average = (this.average * this.inputNumber + req) / (this.inputNumber + 1);

        console.log(responseTimeMs / 1000)
        let groupIndex = Math.floor(responseTimeMs / 1000);
        this.frequencies.set(groupIndex, this.frequencies.get(groupIndex) + 1);

        this.inputNumber += 1;
    }

    getMedian() {
        let medianElement = 0;
        if (this.inputNumber <= 0) {
            return 0;
        }
        if (this.inputNumber == 1) {
            return this.average
        }
        if (this.inputNumber == 2) {
            return this.average
        }
        if (this.inputNumber > 2) {
            medianElement = this.inputNumber / 2;
        }

        let minCumulativeFreq = 0;
        let maxCumulativeFreq = 0;
        let cumulativeFreq = 0;
        let freqGroup = 0;
        for (let i of Array(20).keys()) {
            if (medianElement <= cumulativeFreq + this.frequencies.get(i)) {
                minCumulativeFreq = cumulativeFreq;
                maxCumulativeFreq = cumulativeFreq + this.frequencies.get(i);
                freqGroup = i;
                break;
            }
            cumulativeFreq += this.frequencies.get(i);
        }

        return (((medianElement - minCumulativeFreq) / (maxCumulativeFreq - minCumulativeFreq)) + (freqGroup)) * 1000;
    }

    getAverage() {
        return this.average;
    }

}

Here's the snapshot of the results when I enter the values of

342,654,987,1093,2234,6243,7087,20123

The correct result should be;

Median: 1663.5

• javascript
• median

Share Improve this question Follow edited Jul 25, 2017 at 23:00 msanford 12.2k1313 gold badges7171 silver badges9898 bronze badges asked Jul 25, 2017 at 16:54 Muhammed BayramMuhammed Bayram 63311 gold badge55 silver badges55 bronze badges 6

• maybe look here – Radek Hofman Commented Jul 25, 2017 at 16:57
• 3 To calculate the median, you have to sort the values and pick the middle one. – Pointy Commented Jul 25, 2017 at 16:58
• 2 That's not a median. The median should be in the set. – jmargolisvt Commented Jul 25, 2017 at 16:58
• 1 The Median is the middle number of the sorted list if there are a odd number of values, if there are an even number the median is the mid point or average of the central two values. – Mark B Commented Jul 25, 2017 at 17:06
• 1 Possible duplicate of find median values from array in javascript (8 values or 9 values) – str Commented Jul 25, 2017 at 17:09

 |  Show 1 more comment

17 Answers 17

Sorted by: Reset to default 114

Change your median method to this:

function median(values: number[]): number {

  if (values.length === 0) {
    throw new Error('Input array is empty');
  }

  // Sorting values, preventing original array
  // from being mutated.
  values = [...values].sort((a, b) => a - b);

  const half = Math.floor(values.length / 2);

  return (values.length % 2
    ? values[half]
    : (values[half - 1] + values[half]) / 2
  );

}

fiddle

Here's another solution:

function median(numbers) {
    const sorted = Array.from(numbers).sort((a, b) => a - b);
    const middle = Math.floor(sorted.length / 2);

    if (sorted.length % 2 === 0) {
        return (sorted[middle - 1] + sorted[middle]) / 2;
    }

    return sorted[middle];
}

console.log(median([4, 5, 7, 1, 33]));

2024 TypeScript Approach

const median = (arr: number[]): number | undefined => {
  if (!arr.length) return undefined;
  const s = [...arr].sort((a, b) => a - b);
  const mid = Math.floor(s.length / 2);
  return s.length % 2 ? s[mid] : ((s[mid - 1] + s[mid]) / 2);
};

Notes:

• The type in the function signature (number[]) ensures only an array of numbers can be passed to the function. It could possibly be empty though.
• if (!arr.length) return undefined; checks for the possible empty array, which would not have a median.
• [...arr] creates a copy of the passed-in array to ensure we don't overwrite the original.
• .sort((a, b) => a - b) sorts the array of numbers in ascending order.
• Math.floor(s.length / 2) finds the index of the middle element if the array has odd length, or the element just to the right of the middle if the array has even length.
• s.length % 2 determines whether the array has an even length.
• (s[mid - 1] + s[mid]) / 2 averages the two middle items of the array if the array's length is even.
• s[mid] is the middle item of an odd-length array.

The solutions above - sort then find middle - are fine, but slow on large data sets. Sorting the data first has a complexity of n x log(n).

There is a faster median algorithm, which consists in segregating the array in two according to a pivot, then looking for the median in the larger set. Here is some javascript code, but here is a more detailed explanation

// Trying some array
alert(quickselect_median([7,3,5])); // 2300,5,4,0,123,2,76,768,28]));

function quickselect_median(arr) {
   const L = arr.length, halfL = L/2;
   if (L % 2 == 1)
      return quickselect(arr, halfL);
   else
      return 0.5 * (quickselect(arr, halfL - 1) + quickselect(arr, halfL));
}

function quickselect(arr, k) {
   // Select the kth element in arr
   // arr: List of numerics
   // k: Index
   // return: The kth element (in numerical order) of arr
   if (arr.length == 1)
      return arr[0];
   else {
      const pivot = arr[0];
      const lows = arr.filter((e)=>(e<pivot));
      const highs = arr.filter((e)=>(e>pivot));
      const pivots = arr.filter((e)=>(e==pivot));
      if (k < lows.length) // the pivot is too high
         return quickselect(lows, k);
      else if (k < lows.length + pivots.length)// We got lucky and guessed the median
         return pivot;
      else // the pivot is too low
         return quickselect(highs, k - lows.length - pivots.length);
   }
}

Astute readers will notice a few things:

1. I simply transliterated Russel Cohen's Python solution into JS, so all kudos to him.
2. There are several small optimisations worth doing, but there's parallelisation worth doing, and the code as is is easier to change in either a quicker single-threaded, or quicker multi-threaded, version.
3. This is the average linear time algorithm, there is more efficient a deterministic linear time version, see Russel's post for details, including performance data.

ADDITION 19 Sept. 2019:

One comment asks whether this is worth doing in javascript. I ran the code in JSPerf and it gives interesting results.

• if the array has an odd number of elements (one figure to find), sorting is 20% slower that this "fast median" proposition.

• if there is an even number of elements, the "fast" algorithm is 40% slower, because it filters through the data twice, to find elements number k and k+1 to average. It is possible to write a version of fast median that doesn't do this.

The test used rather small arrays (29 elements in the jsperf test). The effect appears to be more pronounced as arrays get larger. A more general point to make is: it shows these kinds of optimisations are worth doing in Javascript. An awful lot of computation is done in JS, including with large amounts of data (think of dashboards, spreadsheets, data visualisations), and in systems with limited resources (think of mobile and embedded computing).

var arr = {  
  max: function(array) {
    return Math.max.apply(null, array);
  },
  
  min: function(array) {
    return Math.min.apply(null, array);
  },
  
  range: function(array) {
    return arr.max(array) - arr.min(array);
  },
  
  midrange: function(array) {
    return arr.range(array) / 2;
  },

  sum: function(array) {
    var num = 0;
    for (var i = 0, l = array.length; i < l; i++) num += array[i];
    return num;
  },
  
  mean: function(array) {
    return arr.sum(array) / array.length;
  },
  
  median: function(array) {
    array.sort(function(a, b) {
      return a - b;
    });
    var mid = array.length / 2;
    return mid % 1 ? array[mid - 0.5] : (array[mid - 1] + array[mid]) / 2;
  },
  
  modes: function(array) {
    if (!array.length) return [];
    var modeMap = {},
      maxCount = 1,
      modes = [array[0]];

    array.forEach(function(val) {
      if (!modeMap[val]) modeMap[val] = 1;
      else modeMap[val]++;

      if (modeMap[val] > maxCount) {
        modes = [val];
        maxCount = modeMap[val];
      }
      else if (modeMap[val] === maxCount) {
        modes.push(val);
        maxCount = modeMap[val];
      }
    });
    return modes;
  },
  
  variance: function(array) {
    var mean = arr.mean(array);
    return arr.mean(array.map(function(num) {
      return Math.pow(num - mean, 2);
    }));
  },
  
  standardDeviation: function(array) {
    return Math.sqrt(arr.variance(array));
  },
  
  meanAbsoluteDeviation: function(array) {
    var mean = arr.mean(array);
    return arr.mean(array.map(function(num) {
      return Math.abs(num - mean);
    }));
  },
  
  zScores: function(array) {
    var mean = arr.mean(array);
    var standardDeviation = arr.standardDeviation(array);
    return array.map(function(num) {
      return (num - mean) / standardDeviation;
    });
  }
};

const median = (arr) => {
  return arr.slice().sort((a, b) => a - b)[Math.floor(arr.length / 2)];
};

TypeScript Answer 2020:

// Calculate Median 
const calculateMedian = (array: Array<number>) => {
  // Check If Data Exists
  if (array.length >= 1) {
    // Sort Array
    array = array.sort((a: number, b: number) => {
      return a - b;
    });

    // Array Length: Even
    if (array.length % 2 === 0) {
      // Average Of Two Middle Numbers
      return (array[(array.length / 2) - 1] + array[array.length / 2]) / 2;
    }
    // Array Length: Odd
    else {
      // Middle Number
      return array[(array.length - 1) / 2];
    }
  }
  else {
    // Error
    console.error('Error: Empty Array (calculateMedian)');
  }
};

Short and sweet.

Array.prototype.median = function () {
  return this.slice().sort((a, b) => a - b)[Math.floor(this.length / 2)]; 
};

Usage

[4, 5, 7, 1, 33].median()

Works with strings as well

["a","a","b","b","c","d","e"].median()

Simpler & more efficient

const median = dataSet => {
  if (dataSet.length === 1) return dataSet[0]
  const sorted = ([ ...dataSet ]).sort()
  const ceil = Math.ceil(sorted.length / 2)
  const floor = Math.floor(sorted.length / 2)
  if (ceil === floor) return sorted[floor]
  return ((sorted[ceil] + sorted[floor]) / 2)
}

Simple solution:

function calcMedian(array) {
  const {
    length
  } = array;

  if (length < 1)
    return 0;

  //sort array asc
  array.sort((a, b) => a - b);

  if (length % 2) {
    //length of array is odd
    return array[(length + 1) / 2 - 1];
  } else {
    //length of array is even
    return 0.5 * [(array[length / 2 - 1] + array[length / 2])];
  }
}

console.log(2, calcMedian([1, 2, 2, 5, 6]));
console.log(3.5, calcMedian([1, 2, 2, 5, 6, 7]));
console.log(9, calcMedian([13, 9, 8, 15, 7]));
console.log(3.5, calcMedian([1, 4, 6, 3]));
console.log(5, calcMedian([5, 1, 11, 2, 8]));

Simpler, more efficient, and easy to read

1. cloned the data to avoid alterations to the original data.
2. sort the list of values.
3. get the middle point.
4. get the median from the list.
5. return the median.

function getMedian(data) {
    const values = [...data];
    const v   = values.sort( (a, b) => a - b);
    const mid = Math.floor( v.length / 2);
    const median = (v.length % 2 !== 0) ? v[mid] : (v[mid - 1] + v[mid]) / 2; 
    return median;
}

       const medianArr = (x) => {
        let sortedx = x.sort((a,b)=> a-b);
        let halfIndex = Math.floor(sortedx.length/2);
        
         return (sortedx.length%2) ? (sortedx[Math.floor(sortedx.length/2)]) :  ((sortedx[halfIndex-1]+sortedx[halfIndex])/2)
    }
    
    console.log(medianArr([1,2,3,4,5]));
    console.log(medianArr([1,2,3,4,5,6]));

function Median(arr){
    let len = arr.length;
    arr = arr.sort();
    let result = 0;
    let mid = Math.floor(len/2);
    if(len % 2 !== 0){
        result += arr[mid];
    }
    if(len % 2 === 0){
        result += (arr[mid] + arr[mid+1])/2
    }
    return result;
    
}

console.log(`The median is ${Median([0,1,2,3,4,5,6])}`)

function median(arr) {
    let n = arr.length;
    let med = Math.floor(n/2);
    if(n % 2 != 0){
       return arr[med];
    } else{
       return (arr[med -1] + arr[med])/ 2.0
    }
 }
 console.log(median[1,2,3,4,5,6]);

The arr.sort() method sorts the elements of an array in place and returns the array. By default, it sorts the elements alphabetically, so if the array contains numbers, they will not be sorted in numerical order. On the other hand, the arr.sort((a, b) => a - b) method uses a callback function to specify how the array should be sorted. The callback function compares the two elements a and b and returns a negative number if a should be sorted before b, a positive number if b should be sorted before a, and zero if the elements are equal. In this case, the callback function subtracts b from a, which results in a sorting order that is numerical in ascending order.

So, if you want to sort an array of numbers in ascending order, you should use arr.sort((a, b) => a - b), whereas if you want to sort an array of strings alphabetically, you can use arr.sort():

function median(numbers) {
    const sorted = Array.from(numbers).sort((a, b) => a - b);
    const middle = Math.floor(sorted.length / 2);

    if (sorted.length % 2 === 0) {
        return (sorted[middle - 1] + sorted[middle]) / 2;
    }

    return sorted[middle];
}

For better performance in terms of time complexity, use (MaxHeap - MinHeap) to find the median of stream of array.

function findMedian(arr) {
  arr.sort((a, b) => a - b)

  let i = Math.floor(arr.length / 2)
  return arr[i]
}

let result = findMedian([0, 1, 2, 4, 6, 5, 3])
console.log(result)

本文标签： Calculating medianjavascriptStack Overflow