Download STA 120 * Box Plot Quiz

Here is a set of data.
42, 34, 47, 38, 43, 35, 40, 63, 45, 49, 41, 40, 58, 47, 45, 37
1) What is the 5-number summary for this data?
2) Construct a box-plot for this data.
3) What is the IQR?
4) Identify any outliers or explain why there are none.
5) Calculate the mean and standard deviation.
6) Comment on the shape of the distribution of data.
7) Does the relative size of the mean and median agree with what you said about the
shape? Explain
8) What is the percentile rank of the number 38 in this data set?
9) What number is at the 69th percentile?
10) ACT scores have mean 21 and standard deviation 5, and the scores follow a Normal
distribution.
a) What percent of ACT scores are between 11 and 31?
b) What percent of ACT scores are between 16 and 21?
c) What percent of ACT scores are greater than 31?
42, 34, 47, 38, 43, 35, 40, 63, 45, 49, 41, 40, 58, 47, 45, 37
34, 35, 37, 38, 40, 40, 41, 42, 43, 45, 45, 47, 47, 49, 58, 63
34, 35, 37, 38 | 40, 40, 41, 42 | 43, 45, 45, 47 | 47, 49, 58, 63
39
42.5
47
1) What is the 5-number summary for this data?
min = 34, Q1 = 39, med = 42.5, Q3 = 47, max = 63
2) Construct a box-plot for this data.
(your box plot should have labels)
3) What is the IQR?
IQR = Q3 – Q1 = 47 – 39 = 8
4) Identify any outliers or explain why there are none.
Q3 + 1.5IQR = 47 + 1.5(8) = 47 + 12 = 59
Q1 – 1.5IQR = 39 – 1.5(8) = 39 – 12 = 27
63 is an outlier because it is greater than 59
5) Calculate the mean and standard deviation
(34 + 35 + 37 + 38 + 40 + 40 + 41 + 42 + 43 + 45 + 45 + 47 + 47 + 49 + 58 + 63)/16
= 704/16 = 44
x
34
35
37
38
40
40
41
42
43
45
45
47
47
49
58
63
(x-µ)2
100
81
49
36
16
16
9
4
1
1
1
9
9
25
196
361
x-µ
-10
-9
-7
-6
-4
-4
-3
-2
-1
1
1
3
3
5
14
19
x2
1156
1225
1369
1444
1600
1600
1681
1764
1849
2025
2025
2209
2209
2401
3364
3969
∑ 𝑥 = 704 ∑(𝑥 − 𝜇) = 0 ∑(𝑥 − 𝜇)2 = 914 ∑ 𝑥 2 = 31890
∑(𝑥−𝜇)2
𝜎=√
𝑁
914
= √ 16
∑𝑥
= 7.558 or 𝜎 = √
2
2 −(∑ 𝑥)
𝑁
𝑁
31890−
=√
(704)2
16
16
= 7.558
6) Comment on the shape of the distribution of data.
Skewed right
7) Does the relative size of the mean and median agree with what you said about the
shape? Explain
Yes, since the distribution is skewed to the right, we expect the mean to be greater
than the median, and it is! 44 > 42.5
8) 38 has 3 numbers below it (out of 16 numbers), and 3/16 = 0.1875 = 19%. So 38 is at
the 19th percentile.
9) 69% of 16 numbers is about 11 numbers (11.04). So to be at the 69th percentile we
need 11 numbers to be below us, so we need to be in position 12, which is the number 47.
So 47 is at the 69th percentile.
10) a) 95%, b) 34%, c) 2.5%