Pay across a team: $4,500, $4,800, $5,200, $5,500 and $18,000. Arithmetic mean: (4500 + 4800 + 5200 + 5500 + 18000) / 5 = $7,600. Sort the values and take the middle one: 4500, 4800, 5200, 5500, 18000 → median $5,200. Compare: the mean is $2,400 higher than the median. Answer: The median of $5,200 describes typical pay far better — a single high value pulls the mean up.

Mathematics

Statistics

Mean, median, quartiles, standard deviation, weighted mean and points converted into grades.

The mean and the median describe the same data set very differently as soon as one extreme value appears in it. That is why the series calculator gives both at once, together with the quartiles, the range and the standard deviation.

Calculators

Mean, median, quartiles

x̄ = Σxᵢ / n

Numbers (separated by a space or a new line)

Mean of 8 numbers19.375

Median19.5
Quartiles 1 and 314.375 / 23.25
Sum155
Smallest and largest9.5 / 30
Standard deviation6.58
Range20.5

Weighted mean

x̄ = Σ(xᵢ · wᵢ) / Σwᵢ

Values

Weights

Weighted mean4.25

Simple mean4.125
Sum of the weights10
Number of items4

Percentage share of a total

share = x / Σx · 100 %

Part x

Total of the whole

Share14.92%

Remainder85.08%
Value of the remainder211
How many times smaller6.703

Points to percentage and grade

percentage = scored / available · 100 %

Points scored

Points available

Result84.00%

Grade on the standard scalevery good (5)
Points short8
To the 50 % threshold0

Tables and cheat sheets

Points, percentages and grades

typical school thresholds; an individual school may set its own

Result	Grade	Out of 50 points	Out of 100 points
91–100 %	excellent (6)	46–50	91–100
75–90 %	very good (5)	38–45	75–90
60–74 %	good (4)	30–37	60–74
45–59 %	satisfactory (3)	23–29	45–59
30–44 %	pass (2)	15–22	30–44
0–29 %	fail (1)	0–14	0–29

Worked examples with full solutions

Weighted grade average

Grades: tests 4.5 with weight 3, quizzes 3.0 with weight 1, a project 5.0 with weight 2 and participation 4.0 with weight 4.

Multiply the grades by the weights4,5 · 3 + 3,0 · 1 + 5,0 · 2 + 4,0 · 4 = 13,5 + 3 + 10 + 16 = 42,5
Add up the weights3 + 1 + 2 + 4 = 10
Divide42,5 / 10 = 4,25
Compare with the simple mean(4,5 + 3 + 5 + 4) / 4 = 4,125

Answer: The weighted mean is 4.25 — the weights lift the result above the simple mean.

Median vs mean

Pay across a team: $4,500, $4,800, $5,200, $5,500 and $18,000.

Arithmetic mean(4500 + 4800 + 5200 + 5500 + 18000) / 5 = $7,600
Sort the values and take the middle one4500, 4800, 5200, 5500, 18000 → median $5,200
Comparethe mean is $2,400 higher than the median

Answer: The median of $5,200 describes typical pay far better — a single high value pulls the mean up.