Exercise 7.3

1. Say true or false and why?

(i) The difference between the largest and smallest observations in a data set is called the mean.

Solution:

FalseTrue.

(ii) In a bar graph, the bar which has greater length may contains mode.

Solution:

TrueFalse.

(iii) Value of every observation in the data set is taken into account when median is calculated.

Solution:

FalseTrue.

(iv) The median of a set of numbers is always one of the numbers

Solution:

FalseTrue.

2.The monthly income (in rupees) of 7 households in a village are 1200, 1500, 1400, 1000, 1000, 1600, 10000.

3. Observations of a data are 16, 72, 0, 55, 65, 55, 10, and 41. Chaitanya calculated the mode and median without taking the zero into consideration. Did Chaitanya do the right thing?

Solution:

We have to find whether Chaitanya did the right thing or not.

Mode = Observations which occurs more number of times.

From above data,

Observations 55 occurs times.

Mode =

Now,

let's find median.

Here, Number of observations are .

We 1st arrange given data in ascending order.

0, 10 , , 41, , 55, ,

Given data has even number of observations. Hence our medianmode is average of middle numbers.

i.e 4th and th number.

The median = 41 + 552

The median =

is correct, but is wrong.

4. How many distinct sets of three positive integers have a mean of 6, a median of 7, and no mode?

Solution:

For no mode, there is only observations.

Not repeat any observations.

For median , middle number is always because observations are odd numbers (3)

For mean , Sum of all observations are .

Distinct sets of three positive integers are,

(1, 7, ); (2, 7, ); (3, 7, )