Statistics

Mean is the average value

⇒ mean = 6.17

Median is the central value of a data set.

in this question we have 8 different number, and we have to find the median of these numbers.

Let’s write them in ascending order

6.10, 6.10, 6.15, 6.18, 6.20, 6.20, 6.21, 6.25

the two central values are and , i.e., 4^th and 5^th numbers

which are 6.18 and 6.20

⇒

⇒ median = 6.19

The mean and median are approximately same because all of the data are very near to each other.

let’s first write the data in ascending order

13.5,20.5,30.5,33.5,45.5,50.3,53.4,56.3,56.4,56.9,56.9,66.7,

70.6,89.0

there are total 14 values, so the two central values are 7^th and 8^th

term.

⇒

⇒ median = 54.85

mean is the average of all the values

⇒

⇒ 41.9

let the first value be ‘a’ and the common difference be ‘d’.

⇒

Now we know that any k^th term of the AP is given by

a + kd

n is the total number of terms, so the middle term would be .

and its value would be which is equal to the mean.

There are total 35 households.

the median monthly income of these houses will be Monthly Income of which is 18^th term.

we can see that the 18^th value is Rs. 6000 which is the also the monthly income and 8 other households and the other 10 have low income than Rs.6000.

∴ median = Rs.6000

total no. of workers = 32

the median would be the wage of = mean of 16^th and 17^th worker’s wage

⇒ In this question both the 16^th and 17^th worker have a wage of Rs. 700.

∴ median = Rs. 700

Sol. total no. of babies = 70

the median weight of babies would be the average weight of 35^th and 36^th baby.

both babies are having a weight of 3.000 kg

∴ the median weight of all the babies = 3.000 kg

total number of households = 35

∴ the median is the usage of 18^th household.

which lies between 110-120 and in this range there are 8 households.

let’s assume a uniform distribution.

i.e., 14^th household’s usage is 110 and 15^th household’s usage is 110 +

=

⇒ usage of 18^th household =

⇒ usage of 18^th household = 115

∴ 115 is the median value

total no. of children = 40

∴ the median is the mean of marks of 20^th and 21^st child.

both lies in the range of 20-30.

let’s assume a uniform distribution of marks.

i.e., 14^th child has 20 marks and 15^th child has 20 + marks.

⇒ marks of 15^th child =

⇒ marks of 20^th child =

⇒ marks of 20^th child = 25

also, marks of 21^st child =

median =

median =

the total number of workers = 90

⇒ median is the mean of 45^th and 46^th worker’s Income tax

both lies in the range of 4000-5000

let’s assume an equal distribution

33^rd worker → 4000

34^th worker → 4000 +

45^th worker → 4000 + =

45^th worker → 4000 + =

median =

⇒ median =