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subject: Statistics Sample Problems [print this page]

Introduction of statistics sample problem:

The word Statistics has been derived from either Latin word Status or Italian word Statista or German word Statistik or French word Statistique each of which means a political state. Now a days statistics is used for solving or analyzing the problems of the state. It supplies essential information for developmental activities in all the departments.

Sample Problems on Statistics :

problem 1:

A business needs to estimate the true mean annual income of its customer. It randomly samples 150 of its customer. The mean annual income is 60,000 with a standard deviation of 1,250. Find a 95% confidence interval for true mean annual income of the business customers.

Solution:

n = 150

Sample:

Mean = 60000

Standard deviation = 1250

Use z*

Standard deviation becomes 1250/sqrt (150) = 102.12

z* at 95% confidence level = 1.96

60000 +/- 1.96x102.12 or

60000 +/- 200.15

Answer: 59799.85 to 60200.15

Sample statistics problem 2:

In statistics, find the mean, median, mode, Variance, Standard Deviation, Standard Error with solution. 3, 5, 2, 7, 9, 5, 3, 6.

Solution:

Mean:calculate the mean by add all the values in given data and divide it by total number of values.

Solution for calculating the mean by using the formula,

'barx' = '(sumx)/(n)'

= '(3+5+2+7+9+5+3+6)/(8) '

= '(40)/(8)'

Mean = 5

Median: calculate the median, If total number of elements is odd then centre term is median . If even then the median is mean of two numbers.

Arrange the data in Ascending or Descending order

Now the order will be 2,3,3,5,5,6,7,9.

Median = '(5+5)/2'

= 5

Mode: How many times one number is occurred in the data set.

Mode = 3, 5

Variance: Find the average distance of each value and Calculate their average value, square each value and divide it by total number minus one

Solution is calculated by using the variance formula,

S2 = '(sum(x-barx)^2)/(n-1)'

= '"((3-5)^2+(5-5)^2+(2-5)^2+(7-5)^2+(9-5)^2+(5-5)^2+(3-5)^2+(6-5)^2)/(8-1)'

= '(38)/(7)'

S2 = 5.42857143

Standard Deviation: Standard Deviation is the measure of describing the variability and spread of the Data

solution is calculated by using standard deviation formula,

S ='sqrt((sum(x-barx)^2)/(n-1))'

= 'sqrt(5.42857143)'

S = 2.32992949

Standard Error: Divide standard deviation by the square root of N, the sample size.

Solution is calculated by using the standard error using the formula,

Standard error = S n= '(2.32992949)/(sqrt(8))'

= 0.823754471

Sample statistics problem 3:

Find Variance, standard deviation and Standard error 6,5,4,7,8,9,4

Solution :

Mean : 'barx' = '(sum(x)) / n'

= ' (6 + 5 + 7 + 9 + 10 + 8 + 4) / 7'

= 7

Variance : S2 = '(sum(x-barx)^2)/(n-1)'

S2 = '"((6 - 7)^2 + (5 - 7)^2 + (7 - 7)^2 + (9 - 7)^2 + '

= 4.666667

Standard Deviation: S = 'sqrt((sum(x-barx)^2) / (n-1))'

S = 'sqrt(4.66667)'

S = 2.16024767

Standard Error : = 'S / sqrt(n)'

='2.16024767 / sqrt(7) '

Standard Error = 0.816496872

Statistics Sample Problems-practice Problem:

Practice problem 1:

Find Variance, standard deviation and 78, 56, 45,78, 24, 89,57

Answer:

mean = 61

variance = 504.666667

standard deviation = 22.4647873

Practice problem 2:

Find the mean deviation for the mean of the following data :12, 3, 18, 17, 4, 9, 17, 19, 20, 15, 8, 17, 2, 3, 16, 11, 3, 1, 0, 5

Answer: 6.2

Practice problem 3:

In statistics, find the mean, median, mode, Variance, Standard Deviation for getting statistics problem solution. 56, 45, 36, 72, 56, 54, 31

Answer: Mean = 50

Median = 54

Mode = 56

Variance = 192.33333333333

Standard deviation = 13.868429375143

by: Omkar Nayak

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