Question

3. LUXURY CARS collects sample data regarding the number of cars rented per day: 10, 6, 20 a) Calculate the mean, median and mode b) Calculate the range, standard deviation and coefficient of variation

Answer 1

Calculation of Mean

Mean = Sum of terms / Number of terms

= ( 4+10+6+20 ) / 4 = 40 / 4

= 10

Calculation of Median

Median is the middle of a sorted list of numbers. First the data needs to be arranged from least to greatest. If there is an even number of items in the data set, median is found by taking the mean of two middle most numbers.

Here Data set is : 4 , 6 , 10 , 20

6 and 10 are the middle most number.

Median = (6+10) / 2 =16 / 2

= 8

Calculation of Mode

Mode is the number that appears most frequently in a data set.

Data set : 4 , 6 , 10 , 20

Here, no numbers are repeated. So there is no mode

Calculation of Standard Deviation

Standard deviation is the measure of how spread out numbers are. It is the square root of variance.

Lets calculate variance first.

Variance is the average of squared difference from the mean.

Mean = 10

Difference from the mean = (4-10),(6-10),(10-10),(20-10)

= -6 , -4 , 0, 10

Variance = [((-6)^2) + ((-4)^2) + (0^2) + (10^2)] / 4

= ( 36 + 16 + 0 + 100 ) / 4

= 152 / 4

  = 38

Standard deviation = Square root of 38

= 6.16

Calculation of coeffecient of variation

Coeffecient of variation = ( Standard deviation / Mean ) *100

= ( 6.16 / 10 ) *100

= 61.64 %

Please provide feedback if it was helpful. Feel free to comment if you have any doubts.