Question

1. Theamountoftimethatasampleofstudentsspendswatchingtelevisionperdayisgivenbelow.

Students	Time in Minutes
A	40
B	28
C	71
D	47
E	49
F	34
G	40
H	57

1. Computethemean.

2. Computethemedian.

3. Computethestandarddeviation.

4. Computethe75thpercentile.

Answer 1

Ans : Given data set are The amount of time that students spends watching television per day

Students	Time in Minutes
A	40
B	28
C	71
D	47
E	49
F	34
G	40
H	57

A Mean

ΣΧ; mean η

mean = (40+28 + 71 + 47 + 49 + 34 + 40 + 57)/7

mean = 366/8

mean = 45.75

b) Ans :

The median of a data set is found by identifying the middle number in a sorted data set

First we sort the data in ascending order

28,34,40,40,47,49,57,71

Here  an even number of data values in the data set then the median is the average of the two middle numbers.

the middle numbers are the data values at positions 4 and 5 corresponding values are 40 and 47

So, Median = (40+47)/2

Median = 43.5

c) Ans :

To compute the standard deviation using following formula

S= (E(Xi – X)^2 n - 1

s = 1295.5 / 7

s = 13.6040

standard deviation = 13.6040

d) Ans :

75^th percentile :

First we sort the data in ascending order

28,34,40,40,47,49,57,71

the data can be middle into two part

first part is 28,34,40,40

second part is 47,49,57,71

the second data set These are the positions in the data set that are more than the position of the median.

to find median of the second part is 47,49,57,71

Since there is an even number of data values in this data set

middle numbers are the data values 49 and 57

75^th percentile = (49+57)/2

75^th percentile = 53

Final Answer :

mean = 45.75

Median = 43.5

standard deviation = 13.6040

75^th percentile = 53