Question

4. Use the data in the Excel spreadsheet from the tab "Hours of work." The distribution contains information on the number of hours worked per week by each respondent. You must report units in all your responses. a. What is the level of measurement for "hours worked weekly" What is the modal (or mode) number of hours worked weekly? b. What is the mean number of hours worked weekly? c. What is the standard deviation of "hours worked weekly"? d. Report the five-number summary of hours worked weekly. e. Minimum: Lower quartile (Q1): Median (0)

Answer 1

a) The level of measurement for "Hours worked weekly" is Ratio level of measurement.

b) Since there is irregularities in the data, the mode is obtained through grouped method.

Hours of work per week (X)	Frequency (F1)	Frequency (F2)	Frequency (F3)	Frequency (F4)	Frequency (F5)	Frequency (F6)
7	1	2
12	1		3	5
15	2	5			6
20	3		4			10
24	1	8
30	7

The Analysis table is given below

Analysis Table
Column	7	12	15	20	24	30
1						1
2					1	1
3				1	1
4		1	1	1
5			1	1	1
6				1	1	1
Total	0	1	2	4	4	3

From the analysis table the mode of the data is 20.

c) The mean is obtained below in the table

Hours of work per week (X)	Frequency (F)	fX	Cumulative Frequency	Percent	Cumulative Percent	X-Xbar	X-Xbar	f(X-Xbar)
7	1	7	1	6.67%	6.67%	-15.86	251.54	251.54
12	1	12	2	6.67%	13.33%	-10.86	117.94	117.94
15	2	30	4	13.33%	26.67%	-7.86	61.78	123.56
20	3	60	7	20.00%	46.67%	-2.86	8.18	24.54
24	1	24	8	6.67%	53.33%	1.14	1.3	1.3
30	7	210	15	46.67%	100.00%	7.14	50.98	356.86
Total (Sum)	15	343		100.00%			$\sum f(X-Xbar)$	875.74
N=	15						$\frac{\sum f(X-Xbar)}{N-1}$	62.55
N-1=	14						$\sqrt{\frac{\sum f(X-Xbar)}{N-1}}$	7.9
$\sum fX$	343
Mean	22.86	$mean=\frac{\sum fX}{n}$

The mean of the above data = 22.86.

d) The standard deviation of the data = 7.9

e) (i) The minimum = 7.

(ii) The first quartile Q1 is obtained with the following

=((N+1) /4)

= ((15+1) /4)

= ((16) /4)

= 4

The cumulative frequency which its absorbs in is 4 and corresponding X value is 15

Therefore Q1 = 15.

(iii) The first Median is obtained with the following

=((N+1) /2)

=16/2

=8

The cumulative frequency which its absorbs in is 8 and corresponding X value is 24

Therefore Median = 24

(iv) The third quartile Q3 is obtained with the following

=(3(N+1) /4)

=3*16/4

=12

The cumulative frequency which its absorbs in is 15 and corresponding X value is 30

Therefore third quartile Q3 = 30

(v) The maximum = 30

Answer 2

a) The level of measurement for "Hours worked weekly" is Ratio level of measurement.

b) Since there is irregularities in the data, the mode is obtained through grouped method.

Hours of work per week (X)	Frequency (F1)	Frequency (F2)	Frequency (F3)	Frequency (F4)	Frequency (F5)	Frequency (F6)
7	1	2
12	1		3	5
15	2	5			6
20	3		4			10
24	1	8
30	7

The Analysis table is given below

Analysis Table
Column	7	12	15	20	24	30
1						1
2					1	1
3				1	1
4		1	1	1
5			1	1	1
6				1	1	1
Total	0	1	2	4	4	3

From the analysis table the mode of the data is 20.

c) The mean is obtained below in the table

Hours of work per week (X)	Frequency (F)	fX	Cumulative Frequency	Percent	Cumulative Percent	X-Xbar	X-Xbar	f(X-Xbar)
7	1	7	1	6.67%	6.67%	-15.86	251.54	251.54
12	1	12	2	6.67%	13.33%	-10.86	117.94	117.94
15	2	30	4	13.33%	26.67%	-7.86	61.78	123.56
20	3	60	7	20.00%	46.67%	-2.86	8.18	24.54
24	1	24	8	6.67%	53.33%	1.14	1.3	1.3
30	7	210	15	46.67%	100.00%	7.14	50.98	356.86
Total (Sum)	15	343		100.00%			$\sum f(X-Xbar)$	875.74
N=	15						$\frac{\sum f(X-Xbar)}{N-1}$	62.55
N-1=	14						$\sqrt{\frac{\sum f(X-Xbar)}{N-1}}$	7.9
$\sum fX$	343
Mean	22.86	$mean=\frac{\sum fX}{n}$

The mean of the above data = 22.86.

d) The standard deviation of the data = 7.9

e) (i) The minimum = 7.

(ii) The first quartile Q1 is obtained with the following

=((N+1) /4)

= ((15+1) /4)

= ((16) /4)

= 4

The cumulative frequency which its absorbs in is 4 and corresponding X value is 15

Therefore Q1 = 15.

(iii) The first Median is obtained with the following

=((N+1) /2)

=16/2

=8

The cumulative frequency which its absorbs in is 8 and corresponding X value is 24

Therefore Median = 24

(iv) The third quartile Q3 is obtained with the following

=(3(N+1) /4)

=3*16/4

=12

The cumulative frequency which its absorbs in is 15 and corresponding X value is 30

Therefore third quartile Q3 = 30

(v) The maximum = 30