Question

The number of vehicles passing through a bank drive-up line during each 15 minutes was recorded. The results are shown below.

                              28   30   28   31 31

                              28 33   30   38   34

                              34   32 27   34   28

                              23   18   30 30   30

a. Compute the sample mean, median, and the mode for the data on distances driven.

b.  Determine the range, variance, and standard deviation.

c.   Find the first and the third quartiles. State the interquartile range.

Answer 1

Answer)

First we need to arrange the data in ascending order.

18
23
27
28
28
28
28
30
30
30
30
30
31
31
32
33
34
34
34
38

Sample mean = (sum of the observations)/(number of observations)

Sample mean = (18+23...)/20 = 29.85

Median is the middlemost data point of the arranged data = 30

Mode = frequently appearing data point = 30

B)

Range = highest data point - lowest data point = 38-18 = 20.

To find variance, first we need to subtract mean from each and every data point then we need to take.the square and add all the results

= (18-29.85)^2 + (23-29.85)^2..

= 344.55

Now we need to divide 344.55 by n-1 that is by 19.

Variance = 344.55/19 = 18.1342

S.d = √variance = 4.2584

C)

First quartile is the middlemost data point of first half

Q1 = 28

Third quartile is the middlemost data point of second half = 32.5

Interquartile range = Q3 - Q1 = 4.5