The following frequency distribution reports the number of dollars spent for a g

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
420 up to 480 24
480 up to 540 16
540 up to 600 8
600 up to 660 16
660 up to 720 4

(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.

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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