1. Frequency Distribution Table (Mathway)
2. Mean Relative Frequency= ∑fM∑f= 143821 = 68.50 (Mathway)
Mean of all Data = ∑xn= 1484.921 = 70.710
The two values are different because in the first method, the midpoint of every class produces an average value of that class. The sum of the midpoints differ from the sum of all values, and as such they will have different mean values since both will be divided by the total frequency.
3. Chebyshev’s Rule
80 %= 0.8 = 1- [1/(k^2)]; k = square root of (1/0.2) = 2.236
deviation from the mean=k x standard deviation=2.236 x 29.285=65.483
Lower range= 70.710-65.483=5.226
Upper range=70.710+65.483=135.483 (out of range)
The range in which at least 80 percent of the data lie is from 5.226 to135.483. (“Algebra: Probability and Statistics”)
4. To draw a box plot, Q1, Q2, and Q3 must be obtained (Purplemath).
Since n = 21, which is an odd number;
Q1 = average of the two middle values of the ten values below the mean
= (55.85+56.4)/2 = 56.1
Q2 = median of all values = 70
Q3 = average of the two middle values of the ten values above the mean
= (89+90)/2 = 89.5
10 20 30 40 50 60 70 80 90 100 110 120
5. What is the probability of getting an A overall given that the person made above 80 on test 1?
no. of scores with a grade of 80 and above: 8
no. of grade with overall A and score of 80 and above: 5
Probability = 5/8 = 0.625
What is the probability of getting an A on the test given that the overall grade is at least a B?
no. of overall grades of at least B: 16
lowest value of A: 64.1; no. of test equal or above 64.1 = 15
test grade of A with overall grade of A: 10
Probability = (15/16)*(10/15) = 0.625
What is the probability of getting a test grade of A and an overall grade of F?
lowest value of A: 64.1; no. of test equal or above 64.1 = 15
no. of test grade with A and overall grade of F:1
Probability = 1/15 = 0.067
Works Cited
"Algebra: Probability and Statistics." Algebra: Probability and Statistics. N.p., n.d. Web. 23 July 2016.
Mathway. "Statistics Examples | Frequency Distribution | Finding the Mean." Statistics Examples Frequency Distribution | Finding the Mean. N.p., n.d. Web. 23 July 2016.
Purplemath. "Box-and-Whisker Plots: Quartiles, Boxes, and Whiskers." Box-and-Whisker Plots: Quartiles, Boxes, and Whiskers. N.p., n.d. Web. 23 July 2016.
