Show all work Set up a frequency distribution table and calc

Show all work:

Set up a frequency distribution table and calculate the relative frequency for the following quiz scores that Matt achieved in his Algebra course:

Matt’s Quiz Scores: 85, 88, 92, 79, 100, 78, 61, 60, 79, 99, 100, 69, 98, 85, 92, 79, 81, 85, 100, and 100.

Use the following frequency intervals:

60 – 70

70 – 80

80 - 90

90 – 100

Calculate the variance and standard deviation for Matt’s quiz scores.
Suggestion: set the problem up in steps within a table like the textbook illustrates.

Solution

ci f relative frequency x fx x^2 fx^2 60-70 3 0.15 65 195 4225 12675 70-80 4 0.2 75 300 5625 22500 80-90 5 0.25 85 425 7225 36125 90-100 4 0.2 95 380 9025 36100 100-110 4 0.2 105 420 11025 44100 20 1720 151500 E(X)=1720/20=86 V(X)=E(X^2)-E(X))^2 E(X^2)=151500/20=7575 V(X)=7575-(86*86)=179 sd(X)=sqrt(V(X)=13.37909