Answer to Question #122697 in Statistics and Probability for mayuri

Question

Following data of performance scores is available of employees working with a company. You are required to perform the following: a. Make the frequency distribution, Calculate the frequency and the Cumulative frequency b. Calculate the mean, median, quartiles and Mode c. 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

Answer 1

interval Frequency Cumulative frequency

30-40 41 41

41-50 24 65

51-60 33 98

61-70 32 130

71-80 22 152

81-90 26 178

91-100 30 208

To find the mean, the sum of data set should be divided by the number of elements. $\mu =\frac{ 13177 }{ 208 }\approx 63.351$

To find the median, the data should be arranged in order from least to greatest. The median of the data set is 62.

The first quartile  is the median of the lower half of the data in order from least to greatest. It is 45.

The third quartile  is the median of the higher half of the data in order from least to greatest. It is 83.

The mode of the data set is the  number that occurs most frequently in the set. It is 53.

$variance=( Σ(x i −x )^2/(n-1) ​ )$ =((52 - 63.35)² + ... + (66 - 63.35)²)/(208-1)= 428.885

standart deviation=$\sqrt{variance}=\sqrt{428.885}=20.7$