Math Solutions

Create a histogram for test scores with bins [50-60), [60-70), [70-80), [80-90), [90-100]. Adjust bin width.

Draw a box plot for {2, 5, 7, 8, 11, 12, 15, 18, 22, 25, 30}. Show Q1, Q2, Q3, IQR, whiskers, outliers.

Illustrate random, stratified, cluster, and systematic sampling from a population of 1000.

Compute r for {(1,2), (3,6), (5,7), (7,8), (9,10)}. Show scatter plot with r-value.

Are dice rolls {18, 22, 16, 20, 24, 20} consistent with fair dice? Show observed vs expected.

Test if a tutoring program improved scores. Before: mean 65, After: mean 72, n = 15, s = 10.

A company claims mean battery life is 500 hours. A sample of 36 gives mean 490, σ = 30. Test at α = 0.05.

A sample of 50 has mean 72 and σ = 8. Find the 95% confidence interval. Show the interval on the distribution.

If μ = 70 and σ = 10, find the z-score for x = 85. Show where 85 falls on the bell curve.

Draw the standard normal N(0,1). Shade P(-1 < Z < 1) = 68.27%. Interactive σ slider.

Calculate the variance of {10, 12, 14, 16, 18}. Show squared deviations as literal squares.

Find mean, median, and mode of {3, 7, 7, 2, 9, 4, 7, 5}. Show sorted data with markers for each measure.

Generate F(1) through F(15). Show the golden spiral built from Fibonacci squares.

Verify that 28 is a perfect number (1 + 2 + 4 + 7 + 14 = 28). Show the divisor sum animation.

Find x such that x ≡ 2 (mod 3), x ≡ 3 (mod 5), x ≡ 2 (mod 7). Show the CRT construction.

Find integer solutions to 7x + 11y = 1 using the extended Euclidean algorithm. Show lattice points.

Compute φ(36) and use Euler's theorem to find 7^100 mod 36. Show coprime counting.

Find 2^100 mod 13 using Fermat's little theorem. Show the cyclic pattern of powers.

Compute 37 mod 5 and 123 mod 7. Show clock arithmetic and the number wheel visualization.

Test if 7,284 is divisible by 2, 3, 4, 6, 8, 9. Show which rules pass and which fail.