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Name: Quiz 1
You may use your notes and a calculator for this quiz, but online resources
are not permitted. Show all of your work and give complete explanations for
your answers to receive credit.
- For the data set { 53 , 16 , 70 , 7 , 17 , 1 , 26 , 77 , 74 , 94 }. For these 10 values,
find the following:
- The quartiles Q1, Q2, and Q 3
First, reorder the data in increasing order { 1 , 7 , 16 , 17 , 26 , 53 , 70 , 74 , 77 , 94 }.
Q1: The index i is given by i = 1 4 (n^ + 1) =^
11
- Since 2^ < i <^ 3, we
average the second and third values: Q1 = 7+
Q2: The index i is given by i = 1 2 (n^ + 1) =^
11
- Since 5^ < i <^ 6, we
average the fifth and sixth values: Q2 = 25+ 2
Q3: The index i is given by i = 34 (n + 1) = 334. Since 8 < i < 9, we
average the eighth and ninth values: Q3 = 74+77 2.
IQR = Q 3 → Q1 =
151 2 →^
23 2 =^
128 2
- The 40th percentile, P 40
The index i is given by i = 40 100 (n^ + 1) =^
22 5.^ Since 4^ < i <^ 5, we
average the fourth and fifth values P 40 = 7+ 2
- The lower fence and upper fence
lower fence = Q 1 → 1 .5(IQR) = 232 → 1 .5(^1282 ) = → 84 .5.
upper fence = Q3 + 1.5(IQR) = 151 2 + 1.5(
128 2 ) = 171.^5
- Are there any outliers? Explain.
No data value is less than the lower fence or greater than the upper
fence, so there are no outliers.
- (5 points) A study randomly assigns student into one of two groups. The
first group was directed to use social media as they usually do, and the sec-
Name: Quiz 2
You may use your notes and a calculator for this quiz, but online resources
are not permitted. Show all of your work and give complete explanations for
your answers to receive credit.
- For the data set { 53 , 16 , 70 , 7 , 17 , 12 }. For these 6 values, find the fol-
lowing:
- The sample average, the sample variance, and the sample standard de-
viation.
The sample average is given by ¯x = 1 6
i=1 xi^ =^
1 6 (53 + 16 + 70 +
7 + 17 + 12) = 29.16.
The sample variance is given by s 2 = 1 5
i=1(xi→¯x)
2
1 5 ((53→^29 .16)
2
(16→ 29 .16)^2 +(70→ 29 .16)^2 +(7→ 29 .16)^2 +(17→ 29 .16)^2 +(12→ 29 .16)^2 ) =
The sample standard deviation is given by s =
s^2 =
- The z-score of the value x = 12.
The z-score is given by z = x→x¯ s =^
12 → 29. 16
- 86 =^ →^0 .66.^ This means
that 12 is about two-thirds of a standard deviation to the left of ¯x.
- (5 points) Make a histogram of the data using the classes [0, 20], (20, 40],
(40, 60] and (60, 80]. Is the data symmetric, left-skewed, or right-skewed and
why?
Using Chebyshev’s rule, determine the two values a < b, such such that
at least 75% of the data is contained within the interval [a, b]
Chebyshev’s rule says that ↓ 75 percent of the data falls within two standard
deviations of the sample average ¯x = 29.16. This means that a = ¯x → 2 s =
- 16 → 2(25.86) = → 22 .56 and b = ¯x + 2s = 29.16 + 2(25.86) = 80. 88
