# Question 1

## (a)

**Plant A**

** **

**Now,**

Thus, the standard deviation for plant A is 2.6758.

**Plant B**

** **

**Now,**

Thus, the standard deviation for plant B is 2.022.

**Reason**

As the plant B has smaller standard deviation 2.022 compared to plant A 2.6758; therefore, we can say that Plant B sofas production is relatively closer to its mean value and thus are more consistent compared to plant A.

## (b): Precise results

The standard deviation (SD) is the deviation of the values from the mean. While, coefficient of variance (CV) is the ratio of SD to the mean. The SD helps to find out how much production deviate from the average value. Means the average production of sofas for plant A is 11.2 while its SD is 2.6758. This depicts that on average the production of sofas deviates from 2.6758 units. While CV for plant A will be

Thus, the CV for plant A is 23.89%. and for plant B is 20.01%.

The CV is considered to be more accurate comparison tool compared to SD. Because if we increased the value of sample than the SD will also increase while CV tend to be similar.

# Question 2

## (A): Average Revenue

Sales (’00 RO) | No. of Days (f) | Mid-point (x) | F*x |

00-10 | 9 | 5 | 45 |

10-20 | 5 | 15 | 75 |

20-30 | 10 | 25 | 250 |

30-40 | 12 | 35 | 420 |

40-50 | 9 | 45 | 405 |

50-60 | 8 | 55 | 440 |

60-70 | 3 | 65 | 195 |

70-80 | 6 | 75 | 450 |

Total | 62 | | 2280 |

Thus, the average revenue will be 38.

## (b): Mode

The formula for mode is as follow:

Here:

So, by substituting values in the formula:

Thus, the mode for this case is 8.

# Question 3

## (a): Correlation value

**X value**

** **

**Y Values**

** **

X and Y combined

**R Calculation**

As the value of r is near 0.5 so, we can say that there exists moderate correlation between cost and revenue.

## (b)

As the correlation values lie between -1 to 1. So, a value of 1.25 or any value of more than 1 is considered absurd or not correct. This value depicts that there is error in the calculation of r value.

# Question 4

Now the volume of revenue is:

# Question 5

## (a): Sample size

As it is quite difficult to analyze the marks of every student in the Sultanate of Oman. Therefore, a specific sample will be calculated that is mirror of population. And on the basis of this sample results for population can be derived. Because the sample will be exact mirror of the population. There is need of deciding a specific sample size for the research. For this purpose, we with the help of 95% confidence level and 5% margin of level by substituting in the sample formula can find the sample size as the population level is give. As 5% margin of error and 95% confidence level are commonly used numbers so, we use this.

The findings are as follow:

Here

e is margin of error

p standard deviation

n is sample size

## (b): Variables

The dependent variables are the variables that change because of changes occurred in the independent variables. While, independent variables are changed by the researcher. In the given case independent variables are: assignment marks, end term marks, mid term marks, and quiz marks. While dependent variable will be the total marks that can be affected by changes in the independent variables as mentioned.

## (c) Respondents

In the given case respondents are students from different colleges of the Sultanate Oman.

## (d) Data Collection

For the data collection students will be chosen randomly from different colleges. The results and marksheets of the selected students will be the data collection tool. The results of selected students will be recorded for further evaluation.

## (e)

Yes, in this case inferential statistics is applicable. As it will help to draw conclusions based in the analysis. As if the total marks of students are good or high we can say that they are performing good in academic activities.