Measures of Central Tendency in Minutes Worked

The assignment content discusses measures of central tendency for minutes worked per day data. It calculates the mean as 535.5, median as 510, and mode also as 510. The analysis concludes that the mode and median values accurately describe the variable, which is the average minutes worked by each person.

Measures of Central Tendency
Measures of Central Tendency
Laura Peña-Duval
MAT201 / Basic Statistic
May 5, 2017
Professor Qian Liu

Measures of Central Tendency
Q1.
As from the data received in Mod1 SLP it is clear that minutes worked per day are given
which is calculated by the calculating total minutes worked per day as:
For example on first day a person worked from 8:00 am to 5:00 pm including lunch gap
of 30 minutes. Now calculate the total time from 8:00 am to 5:00 pm and then convert
hours into minutes so it comes as 9 hours which is as 9*60 minutes = 540 minutes. Now
subtract the lunch time which is 30 minutes for first day so it comes as 540 -30 = 510
minutes
The table we get from Mod 1 SLP is as:
Work day In time Lunch in
minutes
Out Time Minutes
worked
1 8:00 am 30 5:00 pm 510
2 8:00 am 30 7:00 pm 630
3 8:00 am 45 7:00 pm 615
4 8:00 am 60 5:30 pm 510
5 8:00 am 60 5:30 pm 480
6 8:00 am 45 5:45 pm 540
7 8:00 am 30 6:00 pm 570
8 8:00 am 30 5:00 pm 510
9 8:00 am 30 5:00 pm 510
10 8:00 am 60 5:00 pm 480
Mean = sum of all minutes worked / total no. of working days
 (510+630+615+510+480+540+570+510+510+480)/10
 5355/10
 535.5
Mean = 535.5
Median is the mean value at n/2 and (n+2)/2 positions as n is even that is 10. For
calculating the median first sort the given data in ascending order. Hence we get the list
as
480 480 510 510 510 510 540 570 615 630
Thus n/2 = 10/2 =5 th position
(n+2)/2 = 6th position
mean is thus = (510 + 510 )/2
 1020/2
 510
hence Median = 510
Mode is the most frequent value which is reoccurring several times in the given data and
that is 510
Hence Mode =510
Q2.
The answers got from the above question are like Mean = 535.5 , Median = 510,
Mode=510 which are lower than expected as when the table data minutes values are seen
one could estimate that the answer will come much higher to these values.
Q3.
The measure of central tendency that describes the variable most accurately is the mode
and median value as they are almost similar to the given data value in the table. The
variable that is looked for is the average minutes worked by each person so the value of
mode and median which is 510 is very close to the answer.
Q4.
The Box Plot is drawn as below
EDCA B
495480 630502.5510

Measures of Central Tendency
Here C is the Median value , A is the lower quartile, E is the upper quartile, B is the
median obtained of the first half list and D is the median obtained of second half list.