CBSE Class 10 Statistics Sure Shot Questions Set H

A. Very Short Answer Type Questions

Question. The class marks of distribution are : 6, 10, 14, 18, 22, 26, 30. Find the class size and the class interval.
Answer: Class size = 4, Ist Class interval = 4 – 8

Question. The class marks of distribution are : 47, 52, 57, 62, 67, 72, 77, 82, 87, 92, 97, 102. Determine the class size, the class limits and the true class limits.
Answer: Class size = 5, Class limit for first class = 44.5, 49.4.

Question. Find the range of the following array of data : 70, 65, 71, 36, 55, 61, 62, 41, 40, 39, 35.
Answer: 36

Question. Draw the ogive of the following distribution table:
Class interval: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60
Frequency: 10, 5, 8, 6, 6, 4
Answer: C.f. (10, 15, 23, 29, 35, 39)

Question. The weights (in kilograms) of 25 students are given as follows :
35, 38, 36, 37, 38, 35, 37, 36, 35, 38, 36, 36, 37, 37, 35, 38, 36, 35, 36, 37, 37, 38, 36, 38, 37.
Complete the following frequency table:
Weights: 35, 36, 37, 38
Frequency: –, –, –, –
Answer: 5, 7, 7, 6

Question. The ages of ten students of a group are given below. The ages have been recorded in years and months :
8-6, 9-0, 8-4, 9-3, 7-8, 8-11, 8-7, 9-2, 7-10, 8-8
(i) What is the lowest age?
(ii) What is the highest age?
(iii) Determine the range?
Answer: (i) 7 years, 8 months (ii) 9 years, 3 months (iii) 1 year, 7 months

Question. The marks scored by 55 students in a test are given below :
Marks: 0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35
No. of students: 2, 6, 13, 17, 11, 4, 2
Prepare a cumulative frequency table.
Answer: Cumulative frequencies are: 2, 8, 21, 38, 49, 53, 55.

Question. If the heights of 5 persons are 140 cms, 150 cms, 152 cms, 158 cms and 161 cms respectively, find the mean height.
Answer: 152.2

Question. Find the mean of all factors of 10.
Answer: 4.5

Question. Find the mean of first 10 even natural numbers.
Answer: x + 4

Question. Following are weights (in kg) of 10 new born babies in a hospital on a particular day :
3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6.
Find the mean \( \bar{X} \).
Answer: 4

Question. The number of children in 10 families of a locality are :
2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.
Answer: 3

Question. Calculate the mean for the following distribution:
x : 5 6 7 8 9
f : 4 8 14 11 3
Answer: 7.025

Question. Find the mean of the following distribution:
x : 10 12 20 25 35
f : 3 10 15 7 5
Answer: 20

Question. Find out the mode of the following marks obtained by 15 students in a class:
Marks : 4, 6, 5, 7, 9, 8, 10, 4, 7, 6, 5, 9, 8, 7, 7
Answer: 7 marks

Question. Find the mode from the following data:
125, 175, 225, 125, 225, 175, 325, 125, 375, 225, 125
Answer: 125

Question. Find the mode for the following series:
7.5, 7.3, 7.2, 7.2, 7.4, 7.7, 7.7, 7.5, 7.3, 7.2, 7.6, 7.2
Answer: 7.2

Question. Find arithmetic mean in the following :
Class interval: 0–6, 6–12, 12–18, 18–24, 24–30
Frequency: 7, 5, 10, 12, 6
Answer: 15.75

Question. Find arithmetic mean in the following :
Class interval: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 8, 10, 9, 12, 11
Answer: 26.6

Question. Find arithmetic mean in the following :
Class interval: 0–8, 8–16, 16–24, 24–32, 32–40
Frequency: 5, 9, 10, 8, 8
Answer: 21

Question. Find arithmetic mean in the following :
Class interval: 0–10, 10–20, 20–30, 30–40, 40–50
Frequency: 5, 6, 4, 3, 2
Answer: 20.5

Question. Find the mode of the following series :
Wages (Rs.): 0 – 25, 25 – 50, 50 – 75, 75 – 100, 100 – 125, 125 – above
No. of persons: 10, 30, 40, 25, 20, 15
Answer: Rs.60

Question. Compute the mode for the following data :
Class: 10 – 20, 20 – 30, 30 – 40, 40 – 50, 50 – 60, 60 – 70, 70 – 80, 80 – 90
Frequency: 24, 42, 56, 66, 108, 130, 154, 140
Answer: 76.32

B. Short Answer Type Questions

Question. A cumulative frequency distribution table is given. Convert this into a frequency distribution table.
Marks: below 45, below 60, below 75, below 90
Number of student: 0, 8, 23, 48
Answer: The frequency distribution table is:
Marks: 45-60, 60-75, 75-90
Frequency: 8, 15, 25

Question. Draw a frequency table for the following data:
Class: 111-120, 121-130, 131-140, 141-150, 151-160, 161-170, 171-180, 181-190, 191-200
C.F.: 6, 11, 16, 20, 27, 36, 42, 45, 50
Answer: The frequency table is:
Class: 111-120 (6), 121-130 (5), 131-140 (5), 141-150 (4), 151-160 (7), 161-170 (9), 171-180 (6), 181-190 (3), 191-200 (5)

Question. Construct a c.f. table for the following data :
Class: 4-7, 8-11, 12-15, 16-19, 20-23, 24-27
Frequency: 3, 10, 12, 8, 5, 9
Answer: The cumulative frequency table is:
Class: 4-7 (3), 8-11 (13), 12-15 (25), 16-19 (33), 20-23 (38), 24-27 (47)

Question. The heights (in cm) of 30 students of class IX are given below :
155, 158, 154, 158, 160, 148, 149, 150, 153, 159, 161, 148, 157, 153, 157, 162, 159, 151, 154, 156, 152, 156, 160, 152, 147, 155, 163, 155, 157, 153
Prepare a frequency distribution table with 160-164 as one of the class intervals
Answer: The frequency distribution table can be prepared using class intervals like 144-148, 148-152, 152-156, 156-160, 160-164.

Question. The water bills (in ruppees) of 32 houses in a certain street for the period 1.1.98 to 31.3.98 are given below :
56, 43, 32, 38, 56, 24, 68, 85, 52, 47, 35, 58, 63, 74, 27, 84, 69, 35, 44, 75, 55, 30, 54, 65, 45, 67, 95, 72, 43, 65, 35, 59.
Tabulate the data and present the data as cumulative frequency table using 70-79 as one of the class intervals.
Answer: The data can be tabulated into intervals such as 20-29, 30-39, ..., 90-99 to form a cumulative frequency table.

Question. Read the bar graph shown in Fig. and answer the following questions :
(i) What is the information given by the bar graph?
(ii) How many tickets of Assam State Lottery were sold by the agent ?
(iii) Of which state, were the maximum number of tickets sold?
(iv) State whether true or false.
The maximum number of tickets sold is three times the minimum number of tickets sold.
(v) Of which state were the minimum number of tickets sold?
Answer: (i) Number of tickets of different state lotteries sold by an agent on a day. (ii) 40 (iii) Haryana (iv) False (v) Rajasthan

Question. The following table gives the route length (in thousand kilometers) of the Indian Railways in some of the years :
Year: 1960-61, 1970-71, 1980-81, 1990-91, 2000-2001
Route length (in thousand km): 56, 60, 61, 74, 98
Represent the above data with the help of a bar graph.
Answer: Draw a bar graph with Years on the x-axis and Route length on the y-axis.

Question. The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on the same axes.
Height (in cm): 124 to 128, 128 to 132, 132 to 136, 136 to 140, 140 to 144, 144 to 148, 148 to 152, 152 to 156, 156 to 160, 160 to 164
No. of Children: 5, 8, 17, 24, 16, 12, 6, 4, 3, 1
Answer: Construct the histogram using the heights as class intervals and the frequency polygon by joining midpoints of the bar tops.

Question. The mean of five numbers is 27. If one number is excluded, their mean is 25. Find the excluded number.
Answer: 35

Question. The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them (in kg) are 52, 54, 55, 53, 56 and 54. Find the weight of the seventh student.
Answer: 61 kg

Question. The weights (in kg) of 15 students are : 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.
Answer: 35 kg, 35 kg

A. Long Answer Type Questions

Question. For the following data, construct a histogram:
C.I.: 10-14, 15-19, 20-24, 25-29, 30-34
Frequency: 300, 980, 800, 580, 290
Answer: To draw the histogram, first convert the discontinuous classes into continuous classes (9.5-14.5, 14.5-19.5, etc.).

Question. Draw a histogram for the given data :
C.I.: 25-29, 30-34, 35-39, 40-44, 45-49, 50-54
Frequency: 5, 15, 23, 20, 10, 7
Answer: Convert to continuous classes (24.5-29.5, etc.) and plot frequencies against these intervals.

Question. Find the unknown for the following distribution:
C.I.: 10-20, 20-30, 30-40, 40-50, 50-60, 60-70
Frequency: 12, \( x_2 \), 10, \( x_4 \), \( x_5 \), \( x_5 \)
C.F.: \( x_1 \), 25, \( x_3 \), 43, 48, 48
Answer: \( x_1 = 12, x_2 = 13, x_3 = 35, x_4 = 8, x_5 = 5 \)

Question. To solve a problem, time taken by the students as follows :
37, 31, 27, 18, 59, 45, 54, 40, 32, 43, 39, 49, 45, 40, 59, 53, 52, 50, 40, 59, 60, 23, 21, 20, 22
(a) Construct a frequency distribution data using interval of 10.
(b) Draw a histogram to represent the distribution.
Answer: (a) Frequency table for intervals 10-20, 20-30, etc. (b) Plot these on a histogram.

Question. Construct a frequency polygon for the following data :
C.I.: 0-10, 10-20, 20-30, 30-40, 40-50
Frequency: 85, 40, 45, 25, 5
Answer: Plot midpoints (5, 15, 25, 35, 45) against frequencies and join them with straight lines.

Question. Draw a histogram and a frequency polygon for the following data :
C.I.: 0-50, 51-100, 101-150, 151-200, 201-250, 251-300
Frequency: 12, 18, 27, 20, 17, 06
Answer: Continuous classes conversion and joint plot of histogram and polygon.

Question. Draw a histogram and a frequency polygon from the following data :
C.I.: 21-25, 26-30, 31-35, 36-40, 41-45, 46-50, 51-55, 56-60
Frequency: 21, 22, 50, 110, 87, 51, 18, 23
Answer: Represent frequency distribution on a continuous scale for histogram and polygon.

Question. Thirty children were asked about the number of hours they watched T.V. programmes in the previous week. The results were found as follows :
1 6 2 3 5 12 5 8 4 8
10 3 4 12 2 8 15 1 17 6
3 2 8 5 9 6 8 7 14 12
(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5-10.
(ii) How many children watched television for 15 or more hours a week ?
Answer: (i) Create table with 0-5, 5-10, 10-15, 15-20. (ii) 2 children

Question. Read the bar graph given in fig. and answer the following questions :
(i) What is the information given by the bar graph?
(ii) What is the number of families having 6 members ?
(iii) How many members per family are there in the maximum number of families ? Also tell the number of such families.
(iv) What are the number of members per family for which the number of families are equal? Also, tell the number of such families ?
Answer: (i) Number of families with different number of members in a locality. (ii) 50 (iii) 3, 120 (iv) 9 and 10, 5

Question. The investment (in crores of rupees) of Life Insurance Corporation of India in different sectors are given below :
Sectors: Central Government Securities, State Government Securities, Securities guaranteed by the Government, Private Sectors, Socially oriented sectors (Plan), Socially oriented sectors (Non-Plan)
Investment (in ten crores of ruppes): 45, 11, 23, 18, 46, 11
Represent the above data with the help of a bar graph.
Answer: Plot sectors on x-axis and investment on y-axis.

Question. The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years :
Years: 1982, 1983-84, 1984-85, 1985-86, 1986-87
Value of Exports (in crores of rupees): 300, 325, 475, 450, 550
Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.
Answer: 1986–87

Question. If \( \bar{X} \) is the mean of the ten natural numbers \( x_1, x_2, x_3, \dots, x_{10} \), show that \( (x_1 - \bar{X}) + (x_2 - \bar{X}) + \dots + (x_{10} - \bar{X}) = 0 \).
Answer: 0

Question. Find arithmetic mean in each of the following :
Class-interval: 0–50, 50–100, 100–150, 150–200, 200–250, 250–300
Frequency: 10, 15, 30, 35, 25, 15
Answer: 161.54

Question. Find arithmetic mean in each of the following :
Class-interval: 0–50, 50–100, 100–150, 150–200, 200–250, 250–300
Frequency: 8, 15, 32, 26, 12, 7
Answer: 145

Question. Find arithmetic mean in each of the following :
Class-interval: 10–15, 15–20, 20–25, 25–30, 30–35, 35–40
Frequency: 5, 6, 8, 12, 6, 3
Answer: 24.625

Question. Find arithmetic mean in each of the following :
Class-interval: 18–24, 24–30, 30–36, 36–42, 42–48, 48–54
Frequency: 12, 16, 24, 16, 8, 4