Question

Q1 )Find the 1st quartile, 2nd quartile, third quartile and the interquartile range of the following data set

72, 74, 75, 77, 79, 82, 83, 87, 88, 90, 91, 91, 91, 92, 96, 97, 97, 98, 100

The 1st Quartile :

The 2nd Quartile :

The 3rd Quartile :

The IQR :

Q2)

According to the empirical rule, if a population has a normal distribution, approximately what percentage of values is within one, two and three standard deviation of the mean?

One standard deviation = 68.3%	Yes/No
Two standard deviation = 95.45%	Yes/No
One standard deviation = 95.45%	Yes/No
Three standard deviation = 99.73%	Yes/No
Three standard deviation = 68.3%	Yes/No
Two standard deviation = 99.73% yes/no

Q3)

If the scores on a test have a mean of 26 and a standard deviation of 4, what is the z-score for a score of 18?

The z-score :

Q4)

Consider the data a sample shown below:

1.53   1.50   1.37   1.51   1.55   1.42   1.41   1.48

Find the range, variance, mean and standard deviation

The Mean:

The Standard deviation:

The Range:

Q5)

Of the following Z-score values, which one represents the location closest to the mean?

Select one:

a. Z = - 0.5

b. Z = - 1.0

c. Z = + 0.5

d. Z = + 1.00

e. Z = - 0.1

Answer 1

Observations in the ascending order are :
72,74,75,77,79,82,83,87,88,90,91,91,91,92,96,97,97,98,100

Here, n=19 is odd.

Here, n=19

Q1=(n+1/4)th value of the observation

=(20/4)th value of the observation

=5th value of the observation

=79
Q2=Median= value of (n+1/2)th observation

= value of (19+1/2)th observation

= value of 10th observation

=90

Here, n=19

Q3=(3(n+1)/4)th value of the observation

=(3⋅20/4)th value of the observation

=15th value of the observation

=96

IQR= Q3-Q1= 96-79= 17