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

**PADM 6700Homework Chapters 4,5, and 6 Summer 2021**

#### 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

2 | 5 | 10 | 12 | 4 | 4 | 5 | 17 | 11 | 8 | 12 | 21 | 6 |

21 | 6 | 7 | 13 | 18 | ||||||||

3 |

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.

Bin | Frequency | Rel frequency |

0-4 | 4 | 0.2 |

5-9 | 8 | 0.4 |

10-14 | 5 | 0.25 |

15-19 | 2 | 0.1 |

20+ | 1 | 0.05 |

Total | 20 | 1 |

c. Show the cumulative frequency distribution.

Bin | Frequency | Cumfrequency |

0-4 | 4 | 4 |

5-9 | 8 | 12 |

10-14 | 5 | 17 |

15-19 | 2 | 19 |

20+ | 1 | 20 |

Total | 20 |

d. Show the cumulative relative frequency distribution.

Bin | Frequency | Rel frequency | CumRelfrequency |

0-4 | 4 | 0.2 | 0.2 |

5-9 | 8 | 0.4 | 0.6 |

10-14 | 5 | 0.25 | 0.85 |

15-19 | 2 | 0.1 | 0.95 |

20+ | 1 | 0.05 | 1 |

Total | 20 | 1 |

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:

Rating | Frequency | % |

To a very great extent | 42 | 0.3784 |

To a great extent | 31 | 0.2793 |

To a moderate extent | 19 | 0.1712 |

To some extent | 12 | 0.1081 |

Not at all | 7 | 0.0631 |

Total | 111 | 1 |

**Question 5 5.14 Page 108 (2 Points)
**

Rating | Frequency | % |

Far above expectations | 15 | 0.1145 |

Above expectations | 22 | 0.1679 |

Meets expectations | 77 | 0.5878 |

Below expectations | 9 | 0.0687 |

Below expectations | 8 | 0.0611 |

Total | 131 | 1 |

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__

Xi | Xi-Xmean | (Xi-Xmean)^2 |

0 | -7.07 | 49.9849 |

3 | -4.07 | j |

3 | -4.07 | 16.5649 |

4 | -3.07 | 9.4249 |

5 | -2.07 | 4.2849 |

6 | -1.07 | 1.1449 |

7 | -0.07 | 0.0049 |

8 | 0.93 | 0.8649 |

9 | 1.93 | 3.7249 |

9 | 1.93 | 3.7249 |

10 | 2.93 | 8.5849 |

11 | 3.93 | 15.4449 |

12 | 1.93 | 24.3049 |

12 | 4.93 | 24.3049 |

Σ=99 | Σ=178.9286 |

**Question 7 6.4 Page 118 (2 Points)**

**Question 8 6.10 Page 118 (2 Points)**

__= Σxi/ n = 595/10 =__

**Mean****59.5**

__= Since n is even, the formula for the median is:__

**Median**

**Thus, the median is an average of 40 and 75 which is 57.5****Standard deviation **=

Xi | Xi-Xmean | (Xi-Xmean)^2 |

75 | 15.5 | 240.25 |

20 | -39.5 | 1560.25 |

15 | -44.5 | 1980.25 |

95 | 35.5 | 1260.25 |

30 | -29.5 | 870.25 |

100 | 40.5 | 1640.25 |

40 | -19.5 | 380.25 |

10 | --49.5 | 2450.25 |

90 | 30.5 | 930.25 |

120 | 60.5 | 3660.25 |

595 | 0 | 14972.5 |

** Range **= Maximum-Minimum = 120-10 =

**110**