The problem is to find the mean and the coefficient of variation of a dataset. The data is given in grouped form, with sales ranges, relative frequencies, and frequencies.

1. Problem Description

The problem is to find the mean and the coefficient of variation of a dataset. The data is given in grouped form, with sales ranges, relative frequencies, and frequencies.

2. Solution Steps

First, we need to calculate the midpoints of each sales range. Then we need to use the relative frequencies to find the frequencies. Sum of frequencies is $n$. After that, we can calculate the mean using the formula:

$Mean = \frac{\sum (midpoint * frequency)}{n}$

Finally, the coefficient of variation is calculated using the formula:

$CV = \frac{Standard Deviation}{Mean}$

Since the standard deviation cannot be calculated accurately from the available information, the standard deviation calculation part is ignored. The relative frequencies do not sum to

1.

Sales ranges are: 75-80, 80-85, 85-90, 90-95, 95-100, 100-105, 105-110, 110-

1

1

5. Relative frequencies are: 0.09, 0.12, 0.15, 0.11, 0.20, 0.10, 0.11, 0.

2. Frequencies are: 9, 21, 36, 47, 67, 87, 98, 100

Let's calculate the midpoints of each sales range.

75-80: (75+80)/2 = 77.5

80-85: (80+85)/2 = 82.5

85-90: (85+90)/2 = 87.5

90-95: (90+95)/2 = 92.5

95-100: (95+100)/2 = 97.5

100-105: (100+105)/2 = 102.5

105-110: (105+110)/2 = 107.5

110-115: (110+115)/2 = 112.5

n = 9+21+36+47+67+87+98+100 = 465

Now, calculate $\sum (midpoint * frequency)$:

(77.5*9) + (82.5*21) + (87.5*36) + (92.5*47) + (97.5*67) + (102.5*87) + (107.5*98) + (112.5*100)

= 697.5 + 1732.5 + 3150 + 4347.5 + 6532.5 + 8917.5 + 10535 + 11250

= 47162.5

Mean = 47162.5 / 465 = 101.424731183

Since we cannot calculate Standard Deviation accurately from the information given, we cannot compute the coefficient of variation.

3. Final Answer

Mean = 101.42

Coefficient of Variation: Cannot be determined from the available data.