Statistics Homework: Statistical Analysis of Television Viewing Habits

This assignment solution presents a detailed statistical analysis of television viewing habits. It begins by calculating the mean, median, and mode for two sets of data: one collected by an individual and another collected by their parents. The solution then compares the mean values from both datasets to the expected average, offering insights into the differences. The assignment further identifies the 'minutes' variable as the most relevant independent variable and justifies the use of the mean as the most accurate measure of central tendency due to the absence of outliers. Finally, the solution includes a comprehensive explanation and construction of a box plot, identifying key values like the median, quartiles, and other key data points to visually represent and interpret the data distribution. The assignment demonstrates the application of statistical concepts to real-world scenarios.

Q1.
If the data collected by him for ten days for watching television is taken into
consideration then
Mean = sum of all minutes / total no. of days
 (73 + 80 + 65 + 20 + 69 + 75 + 72 + 73 + 68 + 70)/10
 665/10
 66.5
Thus mean = 66.5 minutes
Median is calculated by sorting the data in ascending or descending order. Sort the data in
ascending order we get
20 65 68 69 70 72 73 73 75 80
Since the no. of days are even so median is calculated at n/2 and (n+2)/2 positions. So we
get n/2 = 10/2 = 5 and (n+2)/ = 12/2 = 6
Now mean is calculated at 5th and 6th position data given hence mean = (70 + 72) /2
 142/2
 71
Thus Median = 71 minutes
For calculating mode we know that mode is the value of data that is most frequently
occurring. Hence in this given data 73 is the most frequent value that occurs mostly.
Thus Mode = 73 minutes
Now if the data collected by his parents are considered then the value of mean , median
and mode are as follows:
Mean = (70 + 80 + 86 + 72 + 69 + 76 + 78 + 74 + 83 + 85)/10
 773/10
 77.3
Thus Mean = 77.3 minutes
Now for Median sort the data in ascending order as
69 70 72 74 76 78 80 83 85 86
n/2 = 5th position which is 76 and (n+2)/2 that is 6th position which is 78
Thus median is equal to = (76 +78)/2
 154/2
 77 minutes
Thus Median = 77 minutes
As there is no value in the data given which is most frequent repeating hence there is no
mode here.
Q2.
If we look over the values got form above question then we see that we received the
mean value as 66.5 minutes for the data collected by him which is much closer to the
probability of 70 minutes but the mean calculated by the data collected by parents is 77.3
minutes which is much higher than the expected average value of watching Television.
Q3.
The variable that has been looked here is the minutes variable as it is an independent
variable which can change while making the experiment. The measure of central
tendency that is most accurately defining this variable of minutes is the value of mean as
there is no outlier in the given data and there are no extreme scores in the distribution.
Q4.
The Box Plot is drawn for the data collected by him is as below where Mean = 66.5
Median =71 and Mode = 73
Now C is the value of median in box plot as 71 then make two half lists separating the
complete list taking the median as 71 so we get two lists as
20 65 68 69 70 and 72 73 73 75 80 thus the median of each half list is as 68 and 73
respectively hence the Box Plot is plotted as below.
In this Box Plot value of five points are as 20 which is A , 68 as B , 71 as C, 73 as D and
80 as D.

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.
EDCA B
68
20 807371