The following frequency distribution reports the number of dollars spent for a g
ID: 2506913 • Letter: T
Question
The following frequency distribution reports the number of dollars spent for a group of people during last week.
Dollars
Frequency
Relative Frequency
Midpoint
Cumulative Frequency
360 up to 420
28
390
28
0.29
420 up to 480
24
450
52
0.25
480 up to 540
16
510
68
0.16
540 up to 600
8
570
76
0.08
600 up to 660
16
630
92
0.16
660 up to 720
4
690
96
0.04
(a) How many people participate in the study?
(b) Calculate the Relative Frequency and enter the results in the above table.
(c) Calculate the Midpoint for each class and enter the results in the above table.
(d) Calculate the Cumulative Frequency and enter the results in the above table.
(e) Construct a Histogram.
(f) Construct a Frequency Polygon.
(g) Construct a Cumulative Frequency Polygon.
Dollars
Frequency
Relative Frequency
Midpoint
Cumulative Frequency
360 up to 420
28
390
28
0.29
420 up to 480
24
450
52
0.25
480 up to 540
16
510
68
0.16
540 up to 600
8
570
76
0.08
600 up to 660
16
630
92
0.16
660 up to 720
4
690
96
0.04
Explanation / Answer
a) number of people who participate in the study= (28+24+16+8+16+4) = 96
b,c,d)
Class Frequency Midpoint Cumulative Frequency Relative Frequency
360-420 28 390 28 0.29
420-480 24 450 52 0.25
480-540 16 510 68 0.16
540-600 8 570 76 0.08
600-660 16 630 92 0.16
660-720 4 690 96 0.04
formulas:
midpoint: (upper class boundary+lower class boundary)/2
cumulative frequency: 28, 24+28=52, 52+16=68, 68+8=76, 76+16=92, 92+4=96
relative frequency: class frequency/total frequency
e)for construction of histogram plot the class in the horizontal axis and frequency density(class frequency/class width) in the vertical axis.[here the frequency densities are: 0.46, 0.40, 0.26, 0.13, 0.26, 0.06 and class width is 60] next, a rectangle is drawn over each class so that its area indicates the corresponding class frequency. in other words, the height of the rectangle becomes equal to the corresponding frequency density. in this manner, a series of adjoining rectangles are erected so that the area covered by this histogram exhibits the total frequency.
f)here the classes are of equal width. the class frequencies are plotted against the class marks(midpoints). finally the plotted points are joined successively by line segments. to get a closed polygon, we take two additional classes, one at each end, which have zero frequencies.
g)for construction of cumulative frequency polygon plot the class in the horizontal axis and the cumulative frequency(less than type) in the vertical axis. here cumulative frequencies are plotted against the upper class boundary as different points which are joined successively by line segments.
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