4 Marks Questions:

1. A frequency distribution of the life times of 400 T.V. picture tubes tested in a tube company is given below. Find the average life of tube.

Solution:

2. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency ‘f’.

Solution:

                                        ⇒ 18(44 + f) = 752 + 20 f

                                         ⇒ 792 + 18 f = 752 + 20 f

                                         ⇒ 792 – 752 = 20 f – 18 f

                                         ⇒ 2f = 40

                                         ⇒ f = 20
 

3. To find out the concentration of SO₂ in the air (in parts per million i.e. ppm), the data was collected for 30 localities in a certain city and is presented below:

Solution:

∴ The mean concentration of SO₂ in the air = 0.099 ppm

4. Thirty women were examined in a hospital by a doctor and their of heart beats per minute were recorded and summarized as shown. Find the mean heart beats per minute for these women, choosing a suitable method.

Solution:

5. The distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify?

 Thus, the average number of wickets taken by these 45 bowlers in one-day cricket is 152.89

Note: Even if the class sizes are unequal, and xi are large numerically, we can still apply the step-deviation method by taking ‘h’ to be a suitable divisor of all the d_i s.

6. A student noted the number of cars passing through a spot on a road for 100 periods; each of 3 minutes, and summarized this in the table given below.

Find the mode of the data.

Solution:

   Here is the maximum class frequency is 20, and the class corresponding to this frequency is 40-50. So, the modal class is 40-50.

7. The median of the following data is 525. Find the values of x and y, if the total frequency is 100.

Solution: 

8. The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table: 

Find the median length of the leaves.

Solution:

2 Marks Questions:

1. Following table shows the weight of 12 students is given. Find the mean weight of the students. 

Solution:

2. If the mean of the following distribution is 6, find the value of ‘p’

Solution:

3. Find the median for the following frequency distribution

Solution:

Here N = 120 ⇒  = 60

We find that the cumulative frequency just greater than   i.e. 60 is 65 and the value of x corresponding to 65 is 5. Therefore Median = 5.

4. Prepare tables to draw less than cumulative frequency curve and greater than cumulative frequency curve for the following frequency distribution (No need to draw graphs)

Solution: 

For Less than cumulative frequency curve

For Greater than cumulative frequency curve

1 Mark Questions:

1. Write the principle to find mean of the grouped data by direct method and explain the terms in the principle.

Solution:

                           

Here f_i = frequencies and x_i = observations

2. Write the principle to find mean of the grouped data by deviation method and explain the terms in the principle.

Solution:

                      

Here A = Assumed Arithmetic Mean, f_i = frequencies and d_i = x_i – A (deviations)

3. Write the principle to find mean of the grouped data by step deviation method and explain the terms in the principle.

Solution:

 

Here A = Assumed Arithmetic Mean, f_i = frequencies and  (deviations), h = height of the class.

4. Write the principle to find mode of the grouped data and explain the terms in the principle.

Solution:

 

                            

Here l = lower boundary of the modal class, h = size of the modal class

f₁ = frequency of the modal class, f₀ = frequency of the class preceding the modal class

f₂ = frequency of the class succeeding the modal class.

5. Write the principle to find median of the grouped data and explain the terms in the principle.

Solution: 

                          

Here l = lower boundary of median class, n = number of observations

cf = cumulative frequency of class preceding the median class

f = frequency of median class, h = class size (size of the median class)

 

Dr. T.S.V.S. Suryanarayana Murthy