Answer to Question #257445 in Statistics and Probability for Shehri

Question

Q.No. 1

 

During 1993, the major earthquakes had Richter magnitudes as shown below.

7.0, 6.2, 7.7, 8.0, 6.4, 6.2, 7.2, 5.4, 6.4, 6.5, 7.2, 5.4

(a) Find mean, median and mode of the above data, and comment it.

(b) Determine interquartile range.

(c) Construct boxplot for outliers.

Q.No. 2

 

The reaction time to a stimulus for a certain test has a mean of 2.5 seconds and a standard deviation of 0.3 second.

Find the z-score for each reaction time and comment on outlier.

(a) 2.7  (b) 3.9  (c) 2.8  (d) 3.1

Answer 1

1.

Least to Greatest Value:

5.4, 5.4, 6.2, 6.2, 6.4, 6.4, 6.5, 7, 7.2, 7.2, 7.7, 8

a)

The mean is the average of a data set:

$\mu=\sum x_i/n=6.63$

The mode is the most common number in a data set: 5.4, 6.2,6.4, 7.2 (appears 2 times)

The median is the middle of the set of numbers:

$(6.4+6.5)/2=6.45$

b)

$IQR=Q_3-Q_1$

$Q_3=7.2,Q_1=6.2$

$IQR=7.2-6.2=1$

c)

2.

outlier in normal distribution are values that are outside the 3σ interval

in our case 3σ interval:

$\mu\pm 3\sigma=(1.6,3.4)$

$z=\frac{x-\mu}{\sigma}$

a)

$x=2.7$ , it is inside 3σ interval

$z=\frac{2.7-2.5}{0.3}=0.67$

b)

$x=3.9$ , it is outside 3σ interval

$z=\frac{3.9-2.5}{0.3}=4.67$

c)

$x=2.8$ , it is inside 3σ interval

$z=\frac{2.8-2.5}{0.3}=1.00$

d)

$x=3.1$ , it is inside 3σ interval

$z=\frac{3.1-2.5}{0.3}=2.00$