Question

The following are given for a set of values:
I.    The values ranged from 40 to 95.
II.   The median value was 79.
III. 25 percent of the values are less than or equal to a value of 60.
IV. 75 percent of the values are less than or equal to 87.

From the above information, the first and third quartile for the data set is.

QQQ

Given the following sample data set:  122     322     452     142     242     312

The total deviation from the sample mean for the data values will be

Answer 1

Given

25 percent of the values are less than or equal to a value of 60.

Hence, first quartile = 60

Also,

75 percent of the values are less than or equal to 87.
Hence, third quartile = 87

Thus,

Answer :

First Quartile = 60

Third Quartile = 87

For the data 122     322     452     142     242     312

n = 6          number of observations in the data

First calculate mean M = (122+322+452+142+242+312)/6 = 265.3333

Standard Deviation =

$\newline =\sqrt{\frac{\sum(x_{i}-M)^{2}}{n-1}} \newline =\sqrt{\frac{\sum(x_{i}-265.3333)^{2}}{6-1}} \newline = \sqrt{15306.67}$

= 123.7201

Total deviation from the sample mean for the data values = 123.7201