NCERT Solutions for Class 10 Maths Exercise 14.3

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NCERT Solutions for Class 10 Maths Exercise 14.3

NCERT Solutions for Class 10 Maths Statistics

Exercise 14.3

1. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.

Ans. For Median:

Here, , then , which lies in interval 125 – 145.

Median class = 125 – 145

So, and

Now, Median =

=

= = 125 + 12 = 137

For Mean:

From given data, Assume mean = 135, Width of the class = 20

=

Using formula, Mean = 135 + 20 (0.102)

= 135 + 2.04 = 137.04

For Mode:

In the given data, maximum frequency is 20 and it corresponds to the class interval 125 – 145.

Modal class = 125 – 145

And and

Mode =

=

=

=

= 125 + 10.76923

= 125 + 10.77

= 135.77

Hence, median, mean and mode of given data is 137 units, 137.04 units and 135.77 units.


NCERT Solutions for Class 10 Maths Exercise 14.3

2. If the median of the distribution given below is 28.5, then find the values of and

Ans.

Here, , then , also, median of the distribution is 28.5, which lies in interval 20 – 30.

Median class = 20 – 30

So, and

……….(i)

Now, Median =

Putting the value of in eq. (i), we get,

Hence the value of and is 8 and 7 respectively.


NCERT Solutions for Class 10 Maths Exercise 14.3

3. A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are only given to persons having age 18 years onwards but less than 60 years.

Ans.

Here, , then , which lies in interval 35 – 40.

Median class = 35 – 40

So, and

Now, Median =

=

=

=

= 35 + 0.7575

= 35 + 0.76 (approx.)

= 35.76

Hence median age of given data is 35.76 years.


NCERT Solutions for Class 10 Maths Exercise 14.3

4. The lengths of 40 leaves of a plant are measured correct to the nearest millimeter and data obtained is represented in the following table. Find the median length of the leaves.

Ans. Since the frequency distribution is not continuous, so firstly we shall make it continuous.

Here, , then , which lies in interval 144.5 – 153.5.

Median class = 144.5 – 153.5

So, and

Now, Median =

=

=

= 144.5 + 2.25

= 146.75

Hence median length of the leaves is 146.75 mm.


NCERT Solutions for Class 10 Maths Exercise 14.3

5. The following table gives the distribution of the life time of 400 neon lamps. Find the median life time of the lamps.

Ans.

Here, , then , which lies in interval 3000 – 3500.

Median class = 3000 – 3500

So, and

Now, Median =

=

=

= 3000 + 406.9767441

= 3000 + 406.98 (approx.)

= 3406.98

Hence median life time of a lamp is 3406.98 hours.


NCERT Solutions for Class 10 Maths Exercise 14.3

6. 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also find the modal size of the surnames.

Ans. For Median:

Here, , then , which lies in interval 7 – 10.

Median class = 7 – 10

So, and

Now, Median =

=

=

= 7 + 1.05

= 8.05

For Mean:

From given data, Assume mean = 8.5, Width of the class = 3

=

Using formula, Mean = 8.5 + 3 (– 0.06) = 8.5 – 0.18 = 8.32

For Mode:

In the given data, maximum frequency is 40 and it corresponds to the class interval 7 – 10.

Modal class = 7 – 10

And and

Mode =

=

=

=

= 7 + 0.88 (approx.)

= 7.88

Hence, median, mean and mode of given data is 8.05 letters, 8.32 letters and 7.88 letters respectively.


NCERT Solutions for Class 10 Maths Exercise 14.3

7. The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Ans.

Here, , then , which lies in interval 55 – 60.

Median class = 55 – 60

So, and

Now, Median =

=

=

= 55 + 1.66666

= 5 + 1.67 (approx.)

= 56.67

Hence median weight of the students are 56.67 kg.

NCERT Solutions for Class 10 Maths Exercise 14.3

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