Short Answer Type Questions
Q.1. The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:
Determine the modal lifetimes of the components. [CBSE 2019 (30/5/1)]
Ans. Here, the maximum class frequency is 61 and the class corresponding to this frequency is 60-80. So, the modal class is 60-80.
Here, l = 60, h = 20 ,f1 = 61, f0 = 52, f2 = 38
Hence, modal lifetime of the components is 65.625 hours
Q.2. The table below shows the salaries of 280 persons. [CBSE 2018]
Calculate the median salary of the data
Therefore, median salary = 13.42 (in thousand Rs.)
Q.3. By changing the following frequency distribution ‘to less than type’ distribution, draw its ogive. [CBSE 2018 (C)]
Long Answer Type Questions
Q.1. If the median of the following frequency distribution is 32.5. Find the values of f1 and f2. [Delhi 2019]
⇒ 15 = 5(6 - f1 )
Q.2. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate [CBSE 2019 (30/5/2)]
Ans. Here, we use step deviation method to find mean.
Let assumed mean A = 70 and class size h = 10
Now, we have
Q.3. 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. [CBSE 2019 (30/1/2)]
Ans. Let the assumed mean A = 16 and class size h = 2, here we apply step deviation method.
Now, we have,
We have, mean = 18, A = 16 and h = 2
⇒ f + 44 = 2f + 24
⇒ f = 44 - 24
⇒ f = 20
Hence, the missing frequency is 20.
Q.4. For the following frequency distribution, draw a cumulative frequency curve (ogive) of 'more than type' and hence obtain the median value. [CBSE 2019(30/5/1)]
Ans. We have cumulative frequency table,
N = 100
∴ Median = 34.34 = 34.3
Q.5. The mean of the following distribution is 18. Find the frequency f of the class 19 - 21. [CBSE 2018]
⇒ 18(40+f) = 704+20f
⇒ 720+18f - 20f + 704
⇒ 720-704 = 20f - 18f
Q.6. The following distribution gives the daily income of 50 workers of a factory: [CBSE 2018]
Convert the distribution above to a less than type cumulative frequency distribution and draw its ogive.