Statistics Answers Explained

In Statistics, a branch of mathematics there are numerous Statistics Problems for which we can calculate Statistics Answers. The following are some of the Statistics math Answers which use stepwise explanation for the given problems.

Consider the scores obtained by 10 students in mathematics test is given as, 55 36 95 73 60 42 25 78 75 62. Calculate and give the statistics Answer for the mean, median, mode and range of the given scores. First we need to arrange the data in the ascending order (preferably). That gives us, 25 36 42 55 60 62 73 75 78 95. The mean of the scores is given by adding the scores and dividing it by the number of scores, which would be, [25+36+42+55+60+62+73+75+78+95]/10 = 601/10=60.1, the median is the middle value in the ordered data set. Here, the data has even number of scores and hence there are two middle values, the median in such case would be the mean of the two middle values, [60+62]/2= 61. The mode is the number that occurs the most number of times, here there is no such score and hence there is no mode for the given data set. Range is the difference of the highest value and the lowest value of the ordered data set, range = 95-25= 70

Find the mean deviation about the mean for the following data: 12,3, 18, 17, 4, 9, 17, 19, 20, 15, 8, 17, 2, 3, 16, 11, 3, 1, 0,  5
Let us first find the mean of the (x bar) of the given data
(xbar) = 1/20*summation(i=1to20)[x(i)]= 200/20 = 10
The respective absolute values of the deviations from the mean , modulus[x(i) – xbar]are
2, 7, 8,7, 6,1,7,9,10,5,2,7,8,7,6,1,7,9,10,5
Summation[(i=1to20)[modulus(x(i) – xbar)] = 124
So, the mean deviation about the mean would be, M.D.(x bar) = 124/20 =6.2

Given the frequency table of the monthly salaries of 20 employees of a company:
Monthly salary(in dollars)   frequency of number of employees[f(i)]
     3500 5
     4000 8
     4200 5
     4300 2
Find the statistics answer of the mean of the salaries of the 20 people and also calculate the standard deviation
Let x(i) be the i th salary and f(i) be the corresponding frequency
Mean of the grouped data can be calculated as mu= summation [x(i)f(i)]/summation[f(i)] which gives us
= [3500x5 + 4000x8 +4200x5 +4300x2]/5+8+5+2
= [17500+32000+21000+8600]/20
= $3955
Now, let us find the standard deviation of the 20 people which can be calculated by the formula
Sqrt of {[summation [x(i)-mu]^2 times f(i)]/summation[f(i)]}.
= sqrt {[5*(3500-3955)^2+ 8*(4000-3955)^2+5*(4200-3955)^2+2*(4300-3955)^2]/20} on simplification, we get 282, rounded to the nearest unit.