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Question (1):
By taking scale 1cm=10% draw a histogram of the following data:
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Answer:
The required histogram representing the given data is shown in graph.
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Question (2):
Draw a histogram of the following frequency table.
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Answer:
On the basis of data, we will first prepare the table of continuous classes and then draw the required histogram.
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Question (3):
Draw a bar diagram and frequency polygon from the table given below on one graph.
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Answer:
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Question (4):
Draw histogram of data given below.
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Answer:
The required histogram for the given data is shown in graph.
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Question (5):
Find the mode of the following using a Histogram:
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Answer:
Mode = 24
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Question (6):
The IQ of 50 students are recorded as follows. Draw a histogram for the data and estimate the mode.
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Answer:
Mode = 107
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Question (7):
The time required in minutes for each of the 50 students to read 20 pages of a book is recorded below:
43 52 47 49 36 48 41 47 50 32 45
48 40 43 48 36 51 44 49 53 37 34
42 47 45 47 44 50 31 48 43 45 44
36 51 51 43 53 46 39 50 42 42 47
38 49 46 40 38 45
With the information, taking classes 30-34, 35-39, 40-44, 45-49 and 50-54,
i) Prepare a frequency distribution table.
ii) Draw a histogram.
iii) Draw a frequency polygon plotting points.
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Answer:
i) The frequency distribution table for the given information is as follows:
(ii) and (iii): The histogram showing the given information and the corresponding frequency polygons are given below:
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Question (8):
Draw a histogram and a frequency polygon for the following frequency distribution.
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Answer:
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Question (9):
Draw a histogram and frequency polygon for the following:
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Answer:
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Question (10):
Draw a Histogram and Frequency polygon for the following:
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Answer:
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Question (11):
The velocity of a car at various times (in hours) of the day are given below:
Draw a velocity time graph for the above data.
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Answer:
The graph is shown in figure.
Here (time, velocity) are plotted as points and then joined by straight coloured line segments.
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Question (12):
The temperature-chart of a patient is given below in figure:
a) Find the temperature of the oatient at (i) 11: 00hours (ii) 15:00hours
b) At what time is the temperature (i) highest (ii) lowest ?
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Answer:
a) Maximum rate of interest was in the year 1996 (12%).
b) Minimum rate of interest was in the years 1995, 1998 and 2000 (8%).
c) Difference is (12-8)% or 4%.
There can be many more situations where you use the skills of reading graphs and make use of that information.
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Question (13):
Given below are the marks of 25 students in a test:
18, 5, 3,2,10,14,15,19,20,22,12,14,8,9,11,12,14,15,6,21,16,17,8,6.
i) Using the class interval 0 - 5, 5 - 10, etc, construct a frequency table.
ii) Find the class marks of each class.
iii) State the length of each class.
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Answer:
i)
ii)
Class mark 
iii)
Length of class = Difference between upper limit and lower limit
Length of each class = 5
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Question (14):
Convert the following distribution table to continuous distribution and prepare cumulative frequency.
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Answer:
To convert discrete classes to continuous classes,
the adjustment factor 
= 0.5
Subtracting 0.5 from lower limits and adding 0.5 to all upper limits, we get continuous classes.
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Question (15):
The following is the pocket money survey of 50 students in a school.
(Pocket money in rupees per month)
From a frequency table with grouping of 10-20, 20-30, 30-40 and so on.
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Answer:
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Question (16):
Using class intervals 0-4, 5-9, 10-14, ... construct the following distribution for the following data.
13, 6, 10, 5, 11, 14, 2, 8, 15, 16, 9, 13, 17, 11, 19, 5, 7, 12, 20, 21, 18, 1, 8, 12, 18
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Answer:
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Question (17):
The sales of a shopkeeper for eight days of july are given
Draw a graph depicting the above data.
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Answer:
The graph is shown in figure
We representing dates on x-axis and sales (in rupees) along y-axis. We plot the ordered pairs (7, 3306), (8, 3392), .....,(14, 3620) and join them by coloured line segments to get the above graph.
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Question (18):
A student got the following marks in 10 subjects. Find the arithmetic mean.
42, 74, 62, 38, 49, 84, 45, 56, 68, 70.
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Answer:
Sum of marks = 42 + 74 + 62 + 38 + 49 + 84 + 45 + 56 + 68 + 70
= 588
Here, n = 10
Mean = 58.8
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Question (19):
Calculate the arithmetic mean for the following scores:
5.2, 6.3, 7.4, 5.5, 6.0, 6.2
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Answer:
Sum of scores = 5.2 + 6.3 + 7.4 + 5.5 + 6.0 + 6.2 = 36.6
Number of scores = 6
Mean = 6.1
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Question (20):
Calculate the arithmetic mean for the following grouped data: 
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Answer:
Mean = 2.9
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Question (21):
Find the Median for the following set of scores:
26, 32, 35, 24, 27, 30, 28, 25, 33, 43.
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Answer:
24, 25, 26, 27, 28, 30, 32, 33, 35, 43
n = 10 (even)
Median = 29
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Question (22):
The Median of the first 10 multiples of five.
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Answer:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Median = Middle-most score
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Question (23):
Find the Mean and Median of:
133, 73, 89, 108, 94, 140, 94, 85, 100, 120
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Answer:
73, 85, 89, 94, 94, 100, 108, 120, 133, 140
(arranged in ascending order)
Mean = 103.6
Median = 97
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Question (24):
Find the Median for the following data:
46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92
If in the data above, 92 is replaced by 19, determine the new median.
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Answer:
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
i) n = 11
Median = 58
ii) If 92 is replaced by 19.
19, 33, 35, 41, 46, 55, 58, 64, 77, 87, 90
Median = 55
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Question (25):
The average score of boys in an examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls.
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Answer:
Let the number of boys be = x
Let the number of girls be = y
Total score of boys = 71x
Total score of girls = 73y
Total score of all students = 71.8 (x + y)
 71.8 (x+y) = 71x + 73y
Therefore the ratio of the number of boys to the number of girls is 3:2.
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Question (26):
The mean of 20 numbers is 20. If 2 is added to each of the first 10 numbers, find the mean of the new set of 20 numbers.
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Answer:
Sum of 20 numbers = 20 x 20 = 400
When 2 is added to the first 10 numbers, the new sum =400+20=420
New Mean = 21
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Question (27):
If the mean of the following distribution is 6, find the value of p.
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Answer:
N = 11
Mean = 6
66 = 53 + 2p
2p = 13
p = 6.5
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Question (28):
Calculate the arithmetic mean of the following frequency distribution:
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Answer:
Mean = 141.875
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Question (29):
Find the Mode of the following marks obtained by 16 students in a subject:
0, 0, 2, 2, 3, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8
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Answer:
Since 5 is the most repeated score,
Mode = 5
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Question (30):
The marks obtained by 102 students in a physics test is given below. Find the average marks.
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Answer:
Mean = 26.08
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Question (31):
The median of the following scores arranged in ascending order is 24. Find x: 11, 12, 14, 18, x+2, x+4, 30, 32, 35, 41.
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Answer:
Since the scores are in ascending order,
11, 12, 14, 18, x+2, x+4, 30, 32, 35, 41
Here n = 10 (even)
Cross - multiplying,
48 = x + 2 + x + 4
48 = 2x + 6
2x = 42
x = 21
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Question (32):
Find the mean of the first five odd natural numbers.
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Answer:
The first five odd natural numbers =1+3+5+7+9=25
n=5
Mean=5
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Question (33):
The weight in kgs of 9 boys are as follows:
54, 59, 63, 53, 73, 49, 50, x, 45. If the average weight is 56 kg, find x.
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Answer:
x = 504 - 446
x = 58
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Question (34):
Calculate the arithmetic mean for the following data:
70, 120, 100, 102, 88, 89, 79, 96.
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Answer:
n = 8
Mean = 93
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Question (35):
Find the median for the following set of scores:
35, 31, 29, 30, 31.5, 45, 25, 26, 33.5.
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Answer:
25, 26, 29, 30, 31, 31.5, 33.5, 35, 45
n = 9 (odd)
= 5th score = 31
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