## DS Assignment Solution Dec 2020

**1st Semester NMIMS Dec 2020 – Rs. 3000/- Only****2nd Semester NMIMS Dec 2020 – Rs. 3000/- Only****3rd Semester NMIMS Dec 2020 – Rs. 3000/- Only****4th Semester NMIMS Dec 2020 – Rs. 2500/- Only**

**Decision Science**

- The data of two variables X and Y is given below:

TABLE BELOW

Y | X |

3 | 45 |

4 | 56 |

5 | 54 |

6 | 56 |

7 | 57 |

6 | 58 |

6 | 67 |

6 | 68 |

7 | 76 |

7 | 76 |

8 | 78 |

9 | 79 |

12 | 80 |

13 | 81 |

15 | 84 |

17 | 89 |

- Calculate the correlation between X and Y
- Apply the regression between X and Y (as dependent variable)
- Estimate the R square
- Predict Y when X = 50

Q2. Following ungrouped data of Sales of a company (in millions) is available

- Make the frequency distribution table with appropiate class interval, frequency, cumulative frequency.
- Calculate the mean, median, mode and quartiles of grouped data.
- Calculate the standard deviation, variance and range
- Make the following diagrams: Histogram, Frequency Polygon, Ogive

3.a. For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. Mr Y owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours.

3.b. The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last (a) Less than 7 months (b) Between 7 and 12 months

### Previous Semester

Q1. Identify the type of the variable in the following table

Table Given Below

Variable | Data Type |

a | Gender |

b | Education Background |

c | Satisfaction |

d | Motivation |

e | Exchange Rate |

f | Gold price |

g | Preference of cars |

h | Teachers Feedback |

i | Grades in post-graduation |

j | Marital Status |

k | Quality of services |

l | Age group |

m | GDP |

n | Interest rate |

o | Twitter comments |

p | Facebook pictures |

Q2. Following data of performance scores is available of employees working with a company. You are required to perform the following:

- Make the frequency distribution, Calculate the frequency and the Cumulative frequency

- Calculate the mean, median, quartiles and Mode

- Calculate the variance and the standard deviation

Table: Performance score of the employees:

TABLE BELOW

52 | 33 | 70 | 95 | 57 | 61 | 47 | 60 |

57 | 64 | 54 | 94 | 38 | 61 | 89 | 48 |

50 | 39 | 94 | 63 | 59 | 31 | 88 | 46 |

68 | 88 | 93 | 48 | 82 | 82 | 72 | 73 |

74 | 70 | 92 | 76 | 98 | 91 | 80 | 68 |

32 | 33 | 31 | 75 | 54 | 48 | 62 | 53 |

36 | 64 | 63 | 66 | 92 | 98 | 91 | 42 |

36 | 54 | 71 | 86 | 84 | 55 | 33 | 43 |

91 | 34 | 64 | 67 | 89 | 78 | 47 | 62 |

97 | 92 | 53 | 56 | 68 | 55 | 36 | 67 |

93 | 42 | 51 | 77 | 36 | 93 | 51 | 66 |

44 | 66 | 63 | 33 | 68 | 79 | 92 | 76 |

83 | 53 | 86 | 76 | 35 | 40 | 43 | 46 |

55 | 41 | 36 | 39 | 42 | 96 | 42 | 77 |

60 | 53 | 38 | 51 | 95 | 56 | 93 | 63 |

48 | 69 | 49 | 33 | 95 | 37 | 83 | 64 |

83 | 62 | 96 | 34 | 85 | 32 | 40 | 85 |

39 | 59 | 77 | 62 | 35 | 34 | 39 | 92 |

54 | 89 | 36 | 45 | 83 | 34 | 86 | 90 |

39 | 61 | 88 | 86 | 55 | 33 | 77 | 40 |

69 | 54 | 30 | 38 | 79 | 77 | 44 | 59 |

95 | 34 | 38 | 91 | 80 | 90 | 58 | 40 |

88 | 45 | 95 | 71 | 80 | 43 | 89 | 53 |

61 | 40 | 31 | 61 | 58 | 53 | 88 | 94 |

91 | 63 | 60 | 94 | 98 | 53 | 53 | 45 |

50 | 34 | 75 | 74 | 90 | 98 | 87 | 66 |

Q3. a. In continuation with the data of performance scores of employees in previous example, perform the following:

- Calculate the range and interquartile range
- Calculate the z scores
- Calculate the skewness and Kurtosis (using excel)
- Comment on the distribution of the data

Q3. b. In the continuation with data of performance scores of employees in previous example, perform the following:

- Make the histogram
- Plot the box-plot diagram
- Plot the frequency polygon
- Plot the Ogive diagram