Chapter SH, Problem 10.9EP

To determine

To find mean, median, mode, range and standard deviation of data after multiply by 3.

Answer to Problem 10.9EP

Mean=53.75

Median=54

Mode=69

Range=33

Standard deviation,

Explanation of Solution

Given information:

Data: 12, 18, 21, 18, 19, 18, 16, 23, 20, 15, 17, 18.

After multiply by 3

Data: 36, 54, 63, 54, 57, 54, 48, 69, 60, 45, 51, 54

Formula used:

  

nis number of frequency

  

  or X_iis mean

Calculation:

  

  

Using mean formula to calculate mean of data

  

On solving,

mean=53.75

Median

Ordered data is 36, 45, 48, 51, 54, 54, 54, 54, 57, 60, 63, 69

n=12

nis even

Middle two terms 54, 54

Median=(54+54)/2 On solving,

Median=54

Mode

Mode is highest frequency of the data

Then, mode=69

Range

Ordered data is 36, 45, 48, 51, 54, 54, 54, 54, 57, 60, 63, 69

Maximum=69

Minimum=36

Range=maximum-minimum

=69-36

On solving,

=33

Standard deviation

  

n=12

Using formula of standard deviation

  

On solving,

  

So,