CBSE Class 10 Maths HOTs Statistics Set D

Multiple Choice Questions

Question. A survey conducted by a group of students is given as
Family Size: \( 1-3 \), \( 3-5 \), \( 5-7 \), \( 7-9 \), \( 9-11 \)
Number of families: \( 7, 8, 2, 2, 1 \)
The mean of the data is
(a) \( 6.8 \)
(b) \( 4.2 \)
(c) \( 5.4 \)
(d) None of these
Answer: (b)

Question. The relationship among mean, median and mode for a distribution is
(a) Mode = Median \( - \) 2mean
(b) Mode = 3 Median \( - \) 2mean
(c) Mode = 2 Median \( - \) 3 mean
(d) Mode = Median \( - \) mean
Answer: (b)

Question. For the following distribution
Class: \( 0-5, 5-10, 10-15, 15-20, 20-25 \)
Frequency: \( 10, 15, 12, 20, 9 \)
The sum of lower limits of the median class and modal class is
(a) \( 15 \)
(b) \( 25 \)
(c) \( 30 \)
(d) \( 35 \)
Answer: (b)

Case Based MCQs

A Tesla car manufacturing industry wants to declare the mileage of their electric cars. For this, they recorded the mileage (km/charge) of 100 cars of the same model. Details of which are given in the following table.
Mileage (km/charge): \( 100-120, 120-140, 140-160, 160-180 \)
Number of Cars: \( 14, 24, 36, 26 \)
Based on the above information, answer the following questions.

Question. The average mileage is
(a) \( 140 \) km/charge
(b) \( 150 \) km/charge
(c) \( 130 \) km/charge
(d) \( 144.8 \) km/charge
Answer: (d)

Question. The modal value of the given data is
(a) \( 150 \)
(b) \( 150.91 \)
(c) \( 145.6 \)
(d) \( 140.9 \)
Answer: (b)

Question. The median value of the given data is
(a) \( 140 \)
(b) \( 146.67 \)
(c) \( 130 \)
(d) \( 136.6 \)
Answer: (b)

Question. Assumed mean method is useful in determining the
(a) Mean
(b) Median
(c) Mode
(d) All of these
Answer: (a)

Question. The manufacturer can claim that the mileage for his car is
(a) \( 144 \) km/charge
(b) \( 155 \) km/charge
(c) \( 165 \) km/charge
(d) \( 175 \) km/charge
Answer: (a)

Short Answer Type Questions

Question. Find the median of the first ten prime numbers.
Answer: 12

Question. An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table.
Number of seats: \( 100-104, 104-108, 108-112, 112-116, 116-120 \)
Frequency: \( 15, 20, 32, 18, 15 \)
Determine the mean number of seats occupied over the flights.
Answer: 109.92

Question. The following distribution gives the daily income of 50 workers of a factory:
Daily income (in \( Rs \)): \( 100-120, 120-140, 140-160, 160-180, 180-200 \)
Number of workers: \( 12, 14, 8, 6, 10 \)
Write the above distribution as ‘less than type’ cumulative frequency distribution. 
Answer:
Daily income (in \( Rs \)) | Cumulative frequency
Less than 120 | 12
Less than 140 | 26
Less than 160 | 34
Less than 180 | 40
Less than 200 | 50

Question. Find the mode of the following frequency distribution. 
Class: \( 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 \)
Frequency: \( 8, 10, 10, 16, 12, 6, 7 \)
Answer: 36

Long Answer Type Questions

Question. Find the mean of the following frequency distribution using assumed mean method.
Class: \( 2-8, 8-14, 14-20, 20-26, 26-32 \)
Frequency: \( 6, 3, 12, 11, 8 \)
Answer: 18.8