The problem is to find the mean and the coefficient of variation for the given data. The data consists of sales intervals, relative frequencies, and frequencies.

1. Problem Description

The problem is to find the mean and the coefficient of variation for the given data. The data consists of sales intervals, relative frequencies, and frequencies.

2. Solution Steps

First, we need to calculate the midpoints ($x_i$) of each sales interval.

- 75-80: $x_1 = (75+80)/2 = 77.5$

- 80-85: $x_2 = (80+85)/2 = 82.5$

- 85-90: $x_3 = (85+90)/2 = 87.5$

- 90-95: $x_4 = (90+95)/2 = 92.5$

- 95-100: $x_5 = (95+100)/2 = 97.5$

- 100-105: $x_6 = (100+105)/2 = 102.5$

- 105-110: $x_7 = (105+110)/2 = 107.5$

- 110-115: $x_8 = (110+115)/2 = 112.5$

Next, calculate the sum of frequencies ($n$).

$n = 9 + 21 + 36 + 47 + 67 + 87 + 48 + 18 = 333$

Then, calculate the sum of $f_i x_i$, where $f_i$ is the frequency for each interval.

- $f_1 x_1 = 9 * 77.5 = 697.5$

- $f_2 x_2 = 21 * 82.5 = 1732.5$

- $f_3 x_3 = 36 * 87.5 = 3150$

- $f_4 x_4 = 47 * 92.5 = 4347.5$

- $f_5 x_5 = 67 * 97.5 = 6532.5$

- $f_6 x_6 = 87 * 102.5 = 8917.5$

- $f_7 x_7 = 48 * 107.5 = 5160$

- $f_8 x_8 = 18 * 112.5 = 2025$

$\sum f_i x_i = 697.5 + 1732.5 + 3150 + 4347.5 + 6532.5 + 8917.5 + 5160 + 2025 = 32562.5$

Calculate the mean ($\bar{x}$).

$\bar{x} = \frac{\sum f_i x_i}{n} = \frac{32562.5}{333} = 97.785$ (approximately)

Next, we need to calculate the standard deviation ($s$). First, we need to calculate $\sum f_i x_i^2$.

- $f_1 x_1^2 = 9 * (77.5)^2 = 9 * 6006.25 = 54056.25$

- $f_2 x_2^2 = 21 * (82.5)^2 = 21 * 6806.25 = 142931.25$

- $f_3 x_3^2 = 36 * (87.5)^2 = 36 * 7656.25 = 275625$

- $f_4 x_4^2 = 47 * (92.5)^2 = 47 * 8556.25 = 401943.75$

- $f_5 x_5^2 = 67 * (97.5)^2 = 67 * 9506.25 = 636918.75$

- $f_6 x_6^2 = 87 * (102.5)^2 = 87 * 10506.25 = 914043.75$

- $f_7 x_7^2 = 48 * (107.5)^2 = 48 * 11556.25 = 554700$

- $f_8 x_8^2 = 18 * (112.5)^2 = 18 * 12656.25 = 227812.5$

$\sum f_i x_i^2 = 54056.25 + 142931.25 + 275625 + 401943.75 + 636918.75 + 914043.75 + 554700 + 227812.5 = 3207031.25$

$s = \sqrt{\frac{\sum f_i x_i^2}{n-1} - \frac{(\sum f_i x_i)^2}{n(n-1)}}$

$s = \sqrt{\frac{3207031.25}{332} - \frac{(32562.5)^2}{333 * 332}}$

$s = \sqrt{9659.733 - \frac{1060210156.25}{110556}}$

$s = \sqrt{9659.733 - 9589.768} = \sqrt{69.965} = 8.365$

Calculate the coefficient of variation (CV).

$CV = \frac{s}{\bar{x}} * 100 = \frac{8.365}{97.785} * 100 = 0.08554 * 100 = 8.554\%$

3. Final Answer

Mean = 97.785

Coefficient of Variation = 8.554%