Math 207 Homework 1
Homework 1
• Due: Monday, Feb 14 at the beginning of class. Write up solutions to the following
problems. Your presentation must be neat, logical, and understandable. You must
show or explain all work and justify your answers with complete sentences. You are
allowed to work with classmates, but each student must write their solutions separately
and indicate with whom they have worked. Your submission should be stapled
and without notebook fringes.
(1) Suppose for a dataset (x1, x2, . . . , x100), you have computed the following:
100X
i=1
xi = 561 and
100X
i=1
x2i = 3859
(a) Compute the mean and standard deviation of the sample (x1, x2, . . . , x100).
(b) Given that x100 = 10, compute the mean and standard deviation of the sample
(x1, x2, . . . , x99).
(2) Suppose a dataset (x1, x2, . . . , x10) has x = 17 and sx = 4.
(a) Find
10P
i=1
xi and
10P
i=1
x2i .
(b) What does Chebyshev’s Theorem tell us about how much of the data is within one,
two and three standard deviations of the mean? State the relevant intervals.
(3) Suppose that you have two datasets (x1, x2, . . . , x50) and (y1, y2, . . . , y150) so that x = 10.4
and y = 11.2. Compute the mean on the combined data set (x1, x2, . . . , x50, y1, y2, . . . , y150).
(4) Suppose we have the following set of quantitative data obtained from a random sample:
x1 = 0, x2 = 1, x3 = 2, x4 = 5, x5 = 7.
(a) Calculate the mean and median of the dataset (x1, x2, . . . , x5).
(b) Calculate the range, variance, and standard deviation of the dataset (x1, x2, . . . , x5).
(c) What does Chebyshev’s Theorem tell us about how much of the data is within one,
two and three standard deviations of the mean? State the relevant intervals.
(d) What are the actual proportions of the data that are within one, two and three
standard deviations of the mean?
(e) Let ui = xi+10 for each i = 1, 2, . . . , 5 and repeat parts (a) and (b) for the dataset
(u1, u2, . . . , u5).
(f) Let wi = 5 · xi for each i = 1, 2, . . . , 5 and repeat parts (a) and (b) for the dataset
(w1, w2, . . . , w5).
Bonus Create a dataset where at least 5% of the data is more than 4 standard
deviations from the mean.
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