Question

In: Statistics and Probability

tens Units 1 5 2 3 4 8 5 2 5 6 9 6 1 3...

tens	Units
1	5
2
3
4	8
5	2 5 6 9
6	1 3 5 4 7 9
7	0 0 4 5 6 9 9
8	1 3 5 6 8 9
9	0 1 2 3 5 9

The table represent a random sample of 31 test scores taken from a large lecture class. Find the following [round to 2 decimal points X. XX]

a) [2 pts] Find the 5 number summary [L, Q1, Q2, Q3, H]

b) [4 pts] Find the mean and standard deviation.

c) [2 pts] Find the IQR

d) [2 pts] Are there any outliers in the test scores? Explain

e)[ 1 pt] Suppose one student in the sample is randomly selected. What is the probability that this student scored less than 50 [leave as a fraction]

Expert Solution

a) [2 pts] Find the 5 number summary [L, Q1, Q2, Q3, H]

5 Numbers Summary
Min	15.00
Q1	63.50
Median (Q2)	75.00
Q3	87.00
Max	99.00

b) [4 pts] Find the mean and standard deviation

Mean	73.19
Standard deviation	17.58

c) [2 pts] Find the IQR

IQR = 23.50

d) [2 pts] Are there any outliers in the test scores? Explain

There is only one outliers is there in the data set

that is , 15

e)[ 1 pt] Suppose one student in the sample is randomly selected. What is the probability that this student scored less than 50 [leave as a fraction]

z = (x - μ) / σ

z = (50-73.19)/17.58 = -1.32

P(Z < -1.32) = 0.0934

Procedures:

Formula Ref:

orchestra answered 2 years ago

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