Math Buddyv1.0

Median calculator

Type or scan a list of numbers. MathBuddy sorts it and finds the middle value step by step.

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What this page covers

  • The median of a list of whole numbers, decimals or negative numbers.
  • Odd and even counts: the single middle value, or the mean of the two middle values.
  • Data given as a frequency table, by finding the middle position with running totals.
  • Not covered here: the mean and mode together (use Mean, median and mode calculator) and the spread of the data (use Standard deviation calculator).

How to enter the problem

  • Type it or paste it. Write the word median, then the numbers separated by commas.
  • Scan it. Fit the one problem in the frame.
  • Choose a photo. Several problems in one photo are solved as a list.
  • Then tap Solve.

Worked examples

Example 1

Problem

Find the median of 15,4,22,9,11\displaystyle 15, 4, 22, 9, 11.

Answer

Verified

The answer is

1111

Explanation

  1. Sort the data
    From smallest to largest: 4,9,11,15,224, 9, 11, 15, 22.
  2. Count the values
    There are n=5n = 5 values, an odd count, so one value sits in the middle.
  3. Find the middle position
    The middle is position n+12=3\frac{n+1}{2} = 3. The third value in the sorted list is 1111.

Example 2

Problem

Find the median of 2.5,4,3.1,6,1.8,5\displaystyle 2.5, 4, 3.1, 6, 1.8, 5.

Answer

Verified

The answer is

3.553.55

Explanation

  1. Sort the data
    1.8,2.5,3.1,4,5,61.8, 2.5, 3.1, 4, 5, 6.
  2. Count the values
    There are n=6n = 6 values, an even count, so two values share the middle: positions 3 and 4.
  3. Read the two middle values
    Position 3 is 3.13.1 and position 4 is 44.
  4. Take their mean
    3.1+42=7.12=3.55\frac{3.1 + 4}{2} = \frac{7.1}{2} = 3.55

Example 3

Problem

A survey records how many pets each student has. The value 1 appears 3 times, 2 appears 5 times, 3 appears 4 times and 4 appears 2 times. Find the median.

Answer

Verified

The answer is

22

Explanation

  1. Count all the data
    n=3+5+4+2=14n = 3 + 5 + 4 + 2 = 14 students, an even count.
  2. Find the middle positions
    With 14 values the middle is between positions 7 and 8.
  3. Use running totals
    Values of 1 fill positions 1 to 3. Values of 2 fill positions 4 to 8. So positions 7 and 8 both hold 22.
  4. Take the mean of the two middle values
    2+22=2\frac{2 + 2}{2} = 2

Common mistakes

  • Taking the middle of the list without sorting it first. In 7,3,9,1,12,57, 3, 9, 1, 12, 5 the unsorted middle pair is 99 and 11, which gives 55 instead of 66.
  • With an even count, picking one of the two middle values instead of their mean.
  • Using the number of rows in a frequency table as nn instead of the total of the frequencies.
  • Counting a repeated value only once. Every copy stays in the sorted list.

Checks, assumptions and limits

  • Check by counting. The same number of values should sit below the median as above it. For the runnable example, three values are below 6 and three are above.
  • The median needs numbers that can be put in order. It does not change if the largest value grows, which is why it resists outliers.
  • MathBuddy can make mistakes. Double check important steps.

Related tasks

Frequently asked questions

With an even count, the median is the mean of the two middle values after sorting. It may be a value that is not in the list, such as 3.55.

Yes. Use the camera on the one problem, or choose a photo. Several problems in one photo are solved as a list.

Yes. Ask a follow-up question in the same thread, for example for the mean or the range of the same data. A typed follow-up needs sign-in.

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