10th Maths Statistics Exercise 14.4 Solutions

Exercise 14.4 Solutions – Class X Mathematics

Exercise 14.4 Solutions

From Class X Mathematics textbook by the State Council of Educational Research and Training, Telangana, Hyderabad

Question 1

The following distribution gives the daily income of 50 workers of a factory.

Daily income (in Rupees) 250-300 300-350 350-400 400-450 450-500
Number of workers 12 14 8 6 10

Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Solution:

Step 1: Convert to less than type cumulative frequency distribution:

Daily income less than (in Rupees) 300 350 400 450 500
Cumulative frequency 12 12+14=26 26+8=34 34+6=40 40+10=50

Question 2

During the medical check-up of 35 students of a class, their weights were recorded as follows:

Weight (in kg) Less than 38 Less than 40 Less than 42 Less than 44 Less than 46 Less than 48 Less than 50 Less than 52
Number of students 0 3 5 9 14 28 32 35

Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.

Solution:

Step 1: The data is already in less than type cumulative frequency form.

Step 2: Drawing the ogive:

Ogive (Less than type) for weights of students

Step 3: Finding median from the graph:

Total number of students (n) = 35

Median position = n/2 = 17.5

From the graph, the x-coordinate corresponding to y=17.5 is approximately 46.5 kg.

Step 4: Verifying using the formula:

The median class is 46-48 (since 17.5 falls in the cumulative frequency of 28)

Using the formula:

\[ \text{Median} = L + \left(\frac{\frac{n}{2} – cf}{f}\right) \times h \]

Where:
L = 46 (lower limit of median class)
cf = 14 (cumulative frequency before median class)
f = 14 (frequency of median class)
h = 2 (class width)

\[ \text{Median} = 46 + \left(\frac{17.5 – 14}{14}\right) \times 2 = 46 + \left(\frac{3.5}{14}\right) \times 2 = 46 + 0.5 = 46.5 \text{ kg} \]

This matches our graphical estimate.

Question 3

The following table gives production yield per hectare of wheat of 100 farms of a village.

Production yield (Quintal/Hectare) 50-55 55-60 60-65 65-70 70-75 75-80
Number of farmers 2 8 12 24 38 16

Change the distribution to a more than type distribution, and draw its ogive.

Solution:

Step 1: Convert to more than type cumulative frequency distribution:

Production yield more than (Quintal/Hectare) 50 55 60 65 70 75
Cumulative frequency 100 100-2=98 98-8=90 90-12=78 78-24=54 54-38=16

Step 2: Drawing the ogive (more than type):

Ogive (More than type) for production yield

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