Practicing Descriptive Statistics


The best way of learning about how to solve Descriptive Statistics problems properly is to PRACTICE. Here you have a couple of step-by-step examples, exclusively for our subscribers

Question 1: HiEd has held 5 recruiting visits around the region so far this year. The number of high school seniors attending these events is given below.


10 15 20 35 20


The average number of high school seniors attending an event is 20.

a. Determine the range for this sample.

b. Determine the standard deviation.

Solution: (a) The range is computed as:

\[Range=Max-Min = {35}-{10} = {25}\]

(b) Finally, the following table shows the required calculations needed to compute the standard deviation:

X

10

100

15

225

20

400

35

1225

20

400

Sum =

100

2350


The sample variance is

\[{{s}^{2}}=\frac{1}{n-1}\left( \sum{X_{i}^{2}}-\frac{{{\left( \sum{{{X}_{i}}} \right)}^{2}}}{n} \right)=\frac{1}{5-1}\left( 2350-\frac{{{\left( 100 \right)}^{2}}}{5} \right)=87.5\]

and also we find that the standard deviation is computed as

\[s=\sqrt{87.5}=9.3541\]



Question 2: The Financial Times/Harris poll is a monthly online poll of adults from six countries in Europe and the united states. The poll conducted in January 2008 included 1015 adults. One of the questions asked was "How would you rate the federal bank in handling the credit problems in the financial markets?" Possible responses were excellent, good, fair, bad, and terrible. The 1015 responses for this question can be found in the data file named fedbank.

a. Construct a frequency distribution.

b. Construct a percent frequency distribution.

c. Construct a bar chart for the percent frequency distribution.

d. comment on how adults in the united states think the federal bank is handling the credit problems in the financial markets.

e. In Spain, 1114 adults were asked, ‘How would you rate the european central bank in handling the credit problems in the financial markets?" The percent frequency distribution obtained is as follows.

Rating Percent Frequency

excellent 0


good 4


fair 46


bad 40


terrible 10


Compare the results obtained in Spain with the results obtained in the United States.

Solution: (a) The following is obtained:

Rating

Frequency

Bad

244

Excellent

20

Fair

528

Good

101

Terrible

122

Grand Total

1015

(b) Now we get:

Rating

Frequency

Percent Frequency

Bad

244

24.04%

Excellent

20

1.97%

Fair

528

52.02%

Good

101

9.95%

Terrible

122

12.02%

Grand Total

1015

100.00%


(c) The following is obtained:

(d) In a big majority, US adults think the fed is handling it in a fair way.

(e) In Spain most adults think that the handling has fair and bad.



Question 3: For the following set of scores:

3, 7, 6, 5, 5, 9, 6, 4, 6, 8, 10, 2, 7, 4, 9, 5, 6, 3, 8

a. Construct a frequency distribution table.

b. Sketch a polygon showing the distribution.

c. Describe the distribution using the following characteristics:

(1) What is the shape of the distribution?

(2) What score best identifies the center (average) for the distribution?

(3) Are the scores clustered together, or are they spread out across the scale?

Solution: (a) The minimum and maximum values obtained from the data provided are

Min = 2


Max = 10



Based on this, we choose the lowest class to be 2. The minimum class width is (10 – 2)/5 = 1.6, so we choose a class width of 2. Hence, the respective lower class limits are computed as Li = 2 + 2*i. The following table shows the frequency table:

Classes

Frequency

Rel. Frequency

Cumulative Frequency

Rel. Cumulative Frequency

2 – 3

3

0.158

3

0.158

4 – 5

5

0.263

8

0.421

6 – 7

6

0.316

14

0.737

8 – 9

4

0.211

18

0.947

10 – 11

1

0.053

19

1



The following histogram is obtained

(b) The following frequency polygon is obtained

(c) (1) The distribution is approximately symmetric.

(2) Since the distribution is roughly symmetric, the mean would be the best measure of central tendency.

(3) The scores are relatively spread across the scale, even though they a bit concentrated about the center.

This tutorial is brought to you courtesy of MyGeekyTutor.com



In case you have any suggestion, please do not hesitate to contact us.

Practicing Descriptive Statistics

log in

reset password

Back to
log in