Frequency Distribution, Mean, Median

Assignment on Frequency distribution, Mean, Median, and Standard Deviation

Question 1 (2 points)

A doctor’s office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over one month

Use classes of 0-4, 5-9, and so on the following:

a. Show the frequency distribution.

0-4 = 4

5-9 = 8

10 – 14 = 5

15 – 19 = 2

20 + = 1

b. Show the relative frequency distribution.

c. Show the cumulative frequency distribution.

d. Show the cumulative relative frequency distribution.

e. What proportion of the patients needing emergency service wait nine (9) minutes or less?

The cumulative relative frequency for 5-9 shows the patients needing emergency service wait nine (9) minutes or lessi.e 0.6. Thus, patients needing emergency service wait nine (9) minutes or less is 60%.

Question 2 5.2 Page 104 (1 Point)

27+31+33+35+40+64+65 = 295/7 = 42.142 (Mean)

Median = (n+1)/2 th value = 4th value

Which is 35 (Median)

The department should send the median age.

Question 3 5.4 Page 104 (1Point)

26+35+51+63+147= 322/5= 64.4 (Mean)

Median = (n+1)/2 th value = 3rd value

Which is 51 (Median)

The army should report the median.

Question 4 5.12 Pages 106 – 107 (2 Points)

a) The level of measurement are on ordinal scale.

b) The percentage distribution is as follows:

Question 5 5.14 Page 108 (2 Points)

Measures of central tendency:

Median = (n+1)/2 th value = 66th value

The 66th value is “meets expectations” and is the median.

c) Since about 50% of the employees have rated “meets expectations”, “below expectations” or “far below expectations”. Thus, the feeling of the head of the Department that at least 90% of them fall into the top two categories is not correct.

Question 6 6.2 Page 118 (1 point)

Median: Since n is even, the formula for the median is:

Average of n/2 th value and (n/2)+th value

Since n=14, median is average of 7th and 8th value

Arranging the data in ascending order,

7th value is 7

And 8th value is 8

Thus, the median is an average of 7 and 8 which is 7.5

Mean= Σxi/ n = 99/14 = 7.07

Standard deviation=