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Count, Sum, Min and Max

Count, sum, minimum, maximum:
four quick data checks

The four simplest summary checks for a list of numbers, how each is found, and how they lead to the average and the range.

Calcylator Editorial Team

Updated · 6 min read

Count, sum, minimum and maximum: four quick checks

For the list 42, 37, 51, 38, 45, 40, 49 and 36, the count is 8, the sum is 338, the minimum is 36 and the maximum is 51. Together these four numbers describe the size, total and extremes of any list.

They are the first things to check on a new set of figures. Each has its own calculator on the site, and each takes a list of numbers as input.

What each check tells you

  • Count: how many values are in the list. It confirms you have all the data and shows the sample size.
  • Sum: the total of all values. It matches a known total such as a till or a bank statement.
  • Minimum: the smallest value, the low point of the data.
  • Maximum: the largest value, the high point.
Quick summary from the four checks =mean = sum ÷ count, range = maximum − minimum
sum:
total of all values
count:
number of values
maximum:
largest value
minimum:
smallest value
The mean and the range are built from these four numbers.

  • Values

    42, 37, 51, 38, 45, 40, 49, 36

  • Count

    8

  • Sum

    338

  • Minimum

    36

  • Maximum

    51

Mean (338 ÷ 8) and range (51 − 36)

42.25 and 15

A worked summary chart

Here is the same list laid out with each calculation.

Summary of 42, 37, 51, 38, 45, 40, 49, 36
CheckHow it is foundResult
CountNumber of values8
SumAdd every value338
MinimumSmallest value36
MaximumLargest value51
MeanSum ÷ count42.25
RangeMaximum − minimum15

When to use these checks

A shop owner counts weekly transactions, sums the takings and notes the best and worst day. A teacher counts the marks entered to be sure no student is missing, then compares the minimum and maximum. A quality inspector uses the minimum and maximum of a batch to see if every part is within limits.

Counting first is a useful habit. If you expect 30 values and the count says 29, a number is missing and every later result would be wrong.

A second example: checking a daily sales list

Imagine five daily sales figures: 1,200, 950, 1,430, 880 and 1,310 rupees. The count is 5, the sum is 5,770, the minimum is 880 and the maximum is 1,430. The mean is 5,770 ÷ 5 = 1,154 and the range is 550.

If the till report says the week's takings were 5,770 rupees, the sum matches and you can trust the list. If it says 5,870, one entry is wrong by 100, and you have found the problem in seconds.

Common mistakes with sum, count, minimum and maximum

  • Leaving out a value when typing the list, which changes the count and the sum.
  • Counting blank cells as values. Only entered numbers belong in the count.
  • Reading the minimum from the first number instead of scanning the whole list.
  • Dividing the sum by the wrong number. The mean uses the count of values, not the maximum.

Common questions

What is the count of a data set?

The count is the number of values in the list. The list 42, 37, 51, 38, 45, 40, 49, 36 has a count of 8. It tells you the size of the sample and is the divisor when you work out the mean.

How do I find the sum of a list of numbers?

Add all the values together. For 42, 37, 51, 38, 45, 40, 49 and 36 the sum is 338. Check by counting the values first, so you know none was skipped while adding.

How do I find the minimum and maximum of a list?

Scan every value, keeping the smallest and the largest seen so far. In 42, 37, 51, 38, 45, 40, 49 and 36 the minimum is 36 and the maximum is 51. Subtract them to get the range of 15.

How are sum and count used to find the average?

Divide the sum by the count. For a sum of 338 across 8 values, the mean is 338 ÷ 8 = 42.25. It is the same value as adding everything and sharing it equally among the values.

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