Question 1 1 / -0
The mean of 12, 10, p, p + 2 and 11 is 9. What is the value of p?
Solution
Mean of 12, 10, p, p + 2 and 11 is 9.
Thus, mean =
9 =
45 = 35 + 2p
2p = 45 – 35
p =
p = 5
Question 2 1 / -0
What is the mean of all prime numbers between 50 and 80 rounded to the nearest whole number?
Solution
The prime numbers between 50 and 80 are:
53, 59, 61, 67, 71, 73 and 79
Total of these 7 prime numbers = 53 + 59 + 61 + 67 + 71 + 73 + 79 = 463
Mean =
= 66.14
66
Question 3 1 / -0
The given data shows the runs scored by Rahul Dravid in the first ten one day matches of his career.
110 82 94 181 186 81 78 93 127 78
The range of the data is ______.
Solution
Range of data is defined as the difference between two extreme observations of distribution
Question 4 1 / -0
Class Interval Frequency 0 - 10 a 10 - 20 b 20 - 30 c 30 - 40 d 40 - 50 f 50 - 60 d 60 - 70 h 70 - 80 i 80 - 90 j 90 - 100 k
If 'f' is the highest frequency of the given data, then which of the following values is nearest to the mode?
Solution
Since 'f' is the highest frequency and succeeding and preceding frequencies are the same, so mode = 45.
Question 5 1 / -0
In an experiment, 9 readings were to be taken. 8 of the readings are as follows:th reading if the median is 106?
Solution
The median is the middle of a sorted list of numbers.
If we have 'n' terms, median, when number of observations is:
Even : Average of (
)
th term and (
)
th term.
Odd : (
)
th term
If we arrange the observations in ascending order;
100, 102, 104, 106, 107, 108, 109, 198
Since the median is 5
th term, which should be 106, so the term that should be added in the series must be less than equal to 106.
So, any number less than or equal to 106 can be the required number.
Question 6 1 / -0
The mean, median and mode for the following set of data are equal.
Solution
Go with the options.
Question 7 1 / -0
The sum of the deviations of a set of values x1 , x2 , ………..xn measured from 50 is -10, and the sum of deviations of the values from 46 is 70. The mean is
Solution
(x
1 - 50) + (x
2 - 50) + …….. + (x
n - 50) = -10
(x
1 + x
2 + …… + x
n ) - 50n = - 10 --------- (1)
(x
1 - 46) + (x
2 - 46) + …… + (x
n - 46) = 70
(x
1 +
x
2 +
……+ x
n ) - 46n = 70 ------ (2)
By solving (1) & (2), we get
50n - 10 = 46n + 70
n = 20
and x
1 + x
2 + …… + x
n = 50 × 20 - 10 = 990
Mean =
=
= 49.5
Question 8 1 / -0
The median of set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set
Solution
Let 9 observations arranged in ascending order be a, b, c, d, e, f, g, h and i.
Question 9 1 / -0
What is the correct relation in the given data?
Solution
-1, 0, 1, 2, 3, 4, 5, 5, 6, 8, 11
Mean =
=
Median =
observation =
observation = 6
th observation
Median = 4
Mode = 5
Mean = Median
Question 10 1 / -0
The average of five consecutive natural numbers is 11. Which is the third largest number out of these five numbers?
Solution
Let the smallest number be x.
Then the 5 consecutive naturals numbers = x, x + 1, x + 2, x + 3 and x + 4.
Sum of the 5 numbers = x + x + 1 + x + 2 + x + 3 + x + 4 = 5x + 10 = 5(x + 2)
Mean =
Average =
= x + 2 = 11
x = 11 - 2 = 9
The numbers are 9, 10, 11, 12 and 13.
Question 11 1 / -0
If the mean of r1 , r2 , r3 and r4 is m, what is the mean of r1 – t, r2 – t, r3 – t and r4 – t?
Solution
Mean of r
1 , r
2 , r
3 and r
4 is m.
r
1 + r
2 + r
3 + r
4 = 4m ….. (1)
Now, mean of r
1 – t, r
2 – t, r
3 – t and r
4 – t =
=
[From (1)]
=
Question 12 1 / -0
What is the mode of the following data of the blood pressure levels of patients (mg/dL) in a month?
Solution
Arrange the data in ascending order,
Question 13 1 / -0
In a set of 991 consecutive natural numbers, if we increase the first 300 numbers by 3 each and decrease the last 300 numbers by 3 each, what will be the effect on the median?
Solution
The median is the middle of a sorted list of numbers.
If we have 'n' terms, median when number of observations is:
Even: Average of Odd: If there are 991 terms, then the median will be
= 496
th term.
Increasing or decreasing the first and last 300 numbers will have no effect on the 496
th term or on the median of the series.
Question 14 1 / -0
For the numbers 11, 15, 9, 14, 12, 15 and 18, which of the following is true?
Solution
Mean =
= 13.4
Arrange the numbers in ascending order:
9, 11, 12, 14, 15, 15, 18
∴
Median = 14
Mode = 15 (the most frequently occurring number)
Thus, Mode > Median > Mean, as 15 > 14 > 13.4
Question 15 1 / -0
What is the value of assumed mean of the given data, if mean of the data is 16?
f i d i 4 -15 5 -10 7 -5 12 0 7 5 5 10
Solution
f i d i f i d i 4 -15 -60 5 -10 -50 7 -5 -35 12 0 0 7 5 35 5 10 50
=
16 = a +
16 = a - 1.5
a = 17.5
Question 16 1 / -0
The following table shows the weights (in lbs, rounded off to the nearest integral value) of newborns in a city hospital on the 4
th of July.
3 6 6 7 7 7 8 8 8 8 9 9 9 10 10
The outlier measurement of 3 lbs is that of a premature delivery and should be ignored for all statistical studies. Of the mean, median, and range of the values listed, which will change the least if the 3 lbs measurement is removed from the data?
Solution
Initial Range = 10 - 3 = 7
Question 17 1 / -0
A book store has a total stock of 25 books of grades 4, 5, 6 and 7. The table below shows the number of books of each grade. Find the number of books of grade 4.
Grade 4 5 6 7 Frequency ? 6 9 6
Solution
Total number of books = 25
Question 18 1 / -0
The average age of 8 persons in a committee is increased by 2 years, when two men aged 35 years and 45 years are substituted by two women. Find the average age of these two women.
Solution
Increase in total age due to substitution is 8 × 2 = 16 years
Total age deducted = 45 + 35 = 80 years
Total age added = 80 + 16 = 96 years
Average age of these two women =
= 48 years
Question 19 1 / -0
The average temperature of Tuesday, Wednesday and Thursday was 42°C. The average temperature of Wednesday, Thursday and Friday was 47°C. If the temperature on Tuesday was 43°C, then the temperature on Friday was
Solution
W + Th + F = 47 × 3 = 141 --- (1)
Question 20 1 / -0
The average height of 30 boys out of a class of 50 is 160 cm. If the average height of the remaining boys is 165 cm, the average height of the whole class (in cm) is
Solution
Sum of heights of 30 boys = 30 × 160 cm = 4800 cm
Question 21 1 / -0
Directions For Questions
Directions: Study the given data carefully and answer the question that follows.
The following graph shows the numbers of consumers (in thousands) who like different brands over the given six years.
...view full instructions
What is the average number of consumers who like Whirlpool over the first five years?
Solution
Required average
thousand = 22 thousand
Question 22 1 / -0
Directions For Questions
Directions: Study the given data carefully and answer the question that follows.
The following graph shows the numbers of consumers (in thousands) who like different brands over the given six years.
...view full instructions
What is the ratio of average number of consumers who like LG to average number of consumers who like Samsung over the first three years?
Solution
For LG:
Average over the first three years =
=
thousand
For Samsung:
Average over the first three years =
=
thousand
Required Ratio =
= 85 : 75 = 17 : 15
Question 23 1 / -0
State 'T' for true and 'F' for false for the following statements.
Solution
(i) This statement is false as the class mark can be found as follows:
Class mark =
(ii) The mean of the first 10 prime numbers is 12.9. This statement is true.
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.
Mean of the first 10 prime numbers =
= 12.9
(iii) This statement is false as histograms are used for continuous class intervals.
(iv) The stored information or data which is already collected from a source is called secondary data.
Question 24 1 / -0
Fill in the blanks with the help of the given table.
(i) The
P of a data set is not affected by the extreme values.
(ii) The mean of two middle terms gives the median when the number of observations is
Q .
(iii) The difference between the upper class limit and the lower class limit is known as
R .
(iv) Mid-value of a class interval is called its
S .
P Q R S A mean odd class mark class size B mode even class size class size C mode even class width class mark D median odd class mark class width
Solution
(i) The mode/median of a data set is not affected by the extreme values. even .class width/class size .class mark .
Question 25 1 / -0
Match the following:
Column A Column B (i) The average age of five teachers is 28 years. If one teacher is excluded, then the mean gets reduced by 2 years. The age of the excluded teacher (in years) is (A) 25 (ii) The data set for ages of 9 employees of a company is: 32, 35, 32, 37, 39, 38, 38, 32, 34. The mode of the given observations is (B) 32 (iii) The median of 10, 20, 15, 30, 35 and 42 is (C) 6 (iv) If the median of 2, m, m + 2, and 10 arranged in ascending order is 7 , the value of 'm' is (D) 36
Solution
(i) Sum of the ages of 5 teachers = 28 × 5 = 140
Sum of the ages of 4 teachers = (28 - 2) × 4 = 104
Age of the excluded teacher = 140 - 104 = 36 years
(ii) 32, 35, 32, 37, 39, 38, 38, 32, 34
When the above observations are arranged in ascending order, we get:
32, 32, 32, 34, 35, 37, 38, 38, 39
Mode is the most repeated observation, which is 32 here.
So, the mode of the given data set is 32.
(iii) Ascending order of the numbers is:
10, 15, 20, 30, 35, 42
Since the number of observations is even, the median will be:
Median =
= 25
(iv) 2, m, m + 2 and 10
Since the number of the given terms is even;
Median = 7 =
14 = 2m + 2
2m = 14 - 2 = 12
m = 6
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