Measures of Central Tendency:The following table presents data on 10 college stu
ID: 3351764 • Letter: M
Question
Measures of Central Tendency:The following table presents data on 10 college students on the following five variables: region of birth (region), opinion of legalization of marijuana (legalization), weekly entertainment expenses (expenses), average number of movies watched each week (movies), and religion (religion).
Region of Birth
Legalization*
Expenses
Movies
Religion
North
6
$33
0
Protestant
North
3
$39
14
Protestant
South
2
$45
10
Catholic
Midwest
1
$47
7
None
North
2
$62
5
Protestant
North
4
$48
1
Jew
South
1
$52
0
Protestant
South
4
$65
14
Other
Midwest
1
$51
3
Other
West
2
$43
4
Catholic
*For the variable legalization 6 = strong support, 3 = neutral, 1 = strong opposition)
Use the data to calculate and report the mean, median and mode (where appropriate) for all five variables. For each variable, show your calculations and interpret each measure of central tendency in a sentence.
Please show your work for each variable and interpratation of measure of central tendency in a sentence.
Region of Birth
Legalization*
Expenses
Movies
Religion
North
6
$33
0
Protestant
North
3
$39
14
Protestant
South
2
$45
10
Catholic
Midwest
1
$47
7
None
North
2
$62
5
Protestant
North
4
$48
1
Jew
South
1
$52
0
Protestant
South
4
$65
14
Other
Midwest
1
$51
3
Other
West
2
$43
4
Catholic
Explanation / Answer
From the given data,
For the variable ‘Region of birth’,
The measure of central tendency appropriate for the variable 'Region of birth' is Mode, the variable being qualitative in nature.
The mode of a set of data is simply the value that appears most frequently in the set.
The data, here, on Region of birth is unimodal with mode 'North' as the region of birth.
For the variable, ‘Legalization’,
The measure of central tendency appropriate for is Mode, the variable being qualitative in nature.
In this case, the dataset for the variable is bimodal, with codes 1 and 2 occurring most frequently (3 times).
It implies that more than half of the population (here, college students) strongly oppose the legalization of marijuana.
For the variable 'Expenses',
a.The mean, is simply the sum of the data values divided by the number of values.
Mean = Sum of the values / Number of values
= ( 33+39+45+47+62+48+52+65+51+43)/10
= 485 / 10
Mean = $48.5
b.The median is the number that falls in the middle position once the data has been organized, arranged smallest to largest.
Arrange the data values in an increasing order
33,39,43,45,47,48,51,52,62,65
Since the number of data values is even, median will be the mean value of numbers found before and after the (n+1)/2 th position.
The number found before 5.5 position is 47 and after 5.5 position is 48.To find their mean value,
(47+48)/2 which is 47.5
Hence the median expenses of the students is $47.5
For the variable ‘Movies’,
a. The mean of no. of movies watched by the students is calculated as:
(0+14+10+7+5+1+0+14+3+4)/ 10 = 5.8
The average number of movies watched by the 10 students is 5.8, rounded as 6 movies per week.
b. The median is obtained as follows:
0, 0, 1, 3, 4, 5, 7, 10, 14, 14
Average of 4 and 5 = (4+5)/2 = 4.5
Median of No. of movies watched per week by students is 4.5
c. Data on ‘Movies' is bimodal with 0 and 14 with equal greatest frequencies.
For the variable ‘Religion’,
The measure of central tendency appropriate for is Mode, the variable being qualitative in nature.
The data, here, on Religion is unimodal with mode 'Protestants' with the greatest frequency (4 times).