Question

Kellie a developmental psychologist measured the number of errors twenty teenagers made in a driving simulator while talking on their cellphones.

Here are the data [1, 2, 5, 2, 1, 3, 1, 4, 1, 2, 1, 25, 1, 4, 1, 40, 1, 2, 1, 1]

6) Calculate the mean, median and mode for this set of data.

7) Which measure of central tendency most accurately describes Kellie’s data? Briefly explain why.  

Answer 1

solution:

Given data

  [1, 2, 5, 2, 1, 3, 1, 4, 1, 2, 1, 25, 1, 4, 1, 40, 1, 2, 1, 1]

Total No.of observations = 20

   6)  

i) calculating mean

Mean =   

=  [1+ 2+ 5+ 2+ 1+ 3+ 1+ 4+ 1+ 2+ 1+ 25+ 1+ 4+ 1 +40+ 1+ 2+ 1+ 1] / 20

= 95 / 20

= 4.75

Mean = 4.75

ii) calculatimg Median

Let's arrange given data set in Ascending order

[ 1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,4,5,25,40 ]

Here, n is even

   Median is the average of (n/2)th and (n/2)+1 th observations = 1+2 / 2 = 1.5

iii) Calculating Mode

Mode is the most frequently occurred value.Here 1 is occurred 10 times

   Mode = 1

7)

--->  When to use Mean : Mean is usually best measure of central tendency to use when your data Distribution is continuous and symmetrical distribution.[ Ex: Normal Distribution ]

----> When to use Mode: Mode is least used measure of central tendency and can be only used only when data dealing with nominal data.

----> When to use Median : The median is usually prefered to other measures of central tendency when your data set is skewed (or) you are dealing with ordinal data

observe graph:

---> As it is not symmetric and further here 25 , 40 are outliers. so, mean is not best central tendency here

--->Here the data positively skewed and the outliers doesn't much effect the median .But some extent mode can also be appropriate here but is best onlu when data is nominal

Median (1.5) is most accurately describes Kellie's data