Chapter 13 Statistics Bits for 10th Class AP Board
Multiple Choice Questions (MCQs)
Question 1.
Mean of first 10 natural numbers is …………… .
A) 5.5
B) 4.5
C) 5
D) 4
Answer:
A) 5.5
Question 2.
Mean of the first five prime numbers ………….. .
A) 5.5
B) 5.6
C) 4.5
D) 3.2
Answer:
B) 5.6
Question 3.
Mode of the data 2, 3, 4, 6, 4, 2, 3, 5, 6, 7, 6 …………….. .
A) 4
B) 3
C) 6
D) 2
Answer:
C) 6
Question 4.
One of the methods determining mode is ………………. .
A) Mode = 3 Median + 2 Mean
B) Mode = 3 Median – 2 Mean
C) Mode = 3 Mean + 2 Median
D) Mode = 3 Mean – 3 Median
Answer:
B) Mode = 3 Median – 2 Mean
Question 5.
If the arithmetic mean of x, x + 3, x + 6, x + 9 and x + 12 is 10 then x = ……………. .
A) 2
B) 4
C) 6
D) 8
Answer:
B) 4
Question 6.
If the median of the data is: 6, 7, x – 2, x, 17, 20 written in ascending order is 16 then x value is ………………. .
A) 13
B) 15
C) 17
D) 19
Answer:
C) 17
Question 7.
Median of first 10 prime numbers ……………. .
A) 10
B) 12
C) 5.5
D) 6.5
Answer:
B) 12
Question 8.
If the mode of the data x, \(\frac{x}{2}\), \(\frac{x}{3}\), \(\frac{x}{4}\), \(\frac{x}{3}\), \(\frac{x}{2}\), \(\frac{x}{3}\) and \(\frac{x}{5}\) is 8 then x = ……………….. .
A) 24
B) 12
C) 16
D) 18
Answer:
A) 24
Question 9.
If the mean of 5, 6, 7, x, 8, y, 14 is 8 then ………….. .
A) x + y = 10
B) x + y = 15
C) x + y = 16
D) x – y =16
Answer:
C) x + y = 16
Question 10.
The mean of n observations is x, if the first observation is increased by 1, second by 2, the third by 3 etc., then the new mean is …………… .
A) x + n
B) \(\frac{x+n}{2}\)
C) \(\frac{2 x+n+1}{2}\)
D) \(\frac{\mathrm{x}-\mathrm{n}+1}{2}\)
Answer:
C) \(\frac{2 x+n+1}{2}\)
Question 11.
The mean of first n natural numbers is \(\frac{5 n}{8}\) then n = …………… .
A) 1
B) 2
C) 3
D) 4
Answer:
D) 4
Question 12.
If mean of observations a1, a2, a, … an is x and each observation is added by b then the new mean is ………….. .
A) a – b
B) a + b
C) \(\frac{a}{b}\)
D) a.b
Answer:
B) a + b
Question 13.
If the mean of observations x1, x2, … xn is m then the mean of x1 – a, x2 – a, x3 – a, … xn – a
A) m – a
B) m + a
C) ma
D) a – m
Answer:
A) m – a
Question 14.
The mean of first n odd natural number is …………… .
A) \(\frac{\mathrm{n}+1}{2}\)
B) \(\frac{\mathrm{n}-1}{2}\)
C) \(\frac{n}{2}\)
D) n
Answer:
D) n
Question 15.
If 40 is removed from the data : 30, 34, 35, 36, 37, 38, 39, 40 then the median decreased by ………….. .
A) 1
B) 0.5
C) 2
D) 1.5
Answer:
B) 0.5
Question 16.
Observe the following tables
1)
ta
2)
ta
For finding Arithmetic Mean by Direct method, the suggested frequency dis-tribution table is …………….. .
A) Only (1) is true.
B) Only (2) is true.
C) (1) and (2) are ture.
D) None of the above.
Answer:
A) Only (1) is true.
Question 17.
Median = l + [latex]\frac{\left(\frac{n}{2}-\mathrm{cf}\right)}{f}[/latex] h, where cf = ……………….. .
A) Cumulative frequency of the class preceding the median class.
B) Cumulative frequency of the median class.
C) Cumulative frequency of the class succeeding the median class.
D) Sum of the frequencies.
Answer:
A) Cumulative frequency of the class preceding the median class.
Question 18.
If \(\overline{\mathbf{x}}\), is the mean of x1, x2, x3, ……….. xn (n items) then \(\sum_{i=1}^n\left(x_1-\bar{x}\right)\) = ………………. .
A) 0
B) n\(\overline{\mathbf{x}}\)
C) \(\frac{x}{n}\)
D) \(\frac{2 \bar{x}}{n}\)
Answer:
A) 0
Question 19.
Mode can be calculated by = l + (\(\frac{f_1-f_0}{2 f_1-f_0-f_2}\)) × h here fi represents
A) frequency of the modal class
B) frequency of class preceding modal class
C) frequency of class succeeding in the modal class
D) Cumulative frequency of the class preceding the modal class
Answer:
A) frequency of the modal class
Question 20.
The x – coordinate of the point of intersection of the two ogives of grouped data is …………….. .
A) median of the data
B) mode of the data
C) mean of the data
D) average of mid values of the data
Answer:
A) median of the data
Question 21.
3, 2, 4, 3, 5, 2, x, 6. If the mode of this data is 3, then x = …………… .
A) 4
B) 3
C) 2
D) 5
Answer:
B) 3
Question 22.
For the terms, x + 1, x + 2, x – 1, x + 3 and x – 2 (x ∈ N) if the median of the data is 12, then x = …………….. .
A) 9
B) 10
C) 11
D) 13
Answer:
C) 11
Question 23.
Which one of the following is NOT a measure of central tendency ?
A) Mean
B) Median
C) Range
D) Mode
Answer:
C) Range
Question 24.
The most stable measure of central tendency is
A) Mean
B) Median
C) Mode
D) Deviation
Answer:
A) Mean
Question 25.
If the less than type Ogive and more than type Ogive intersect each other at (42, 18), then the median of the given data is
A) 60
B) 42
C) 18
D) 26
Answer:
B) 42
Question 26.
Mean of certain number of observations is \(\overline{\mathbf{x}}\). If each observation is divided by m(m 1 0) and then increased by n, then the mean of new observation is
A) \(\frac{\bar{x}}{n}\) + m
B) \(\overline{\mathbf{x}}\) + \(\frac{n}{m}\)
C) \(\overline{\mathbf{x}}\) + \(\frac{m}{n}\)
D) \(\frac{\bar{x}}{m}\) + n
Answer:
D) \(\frac{\bar{x}}{m}\) + n
Question 27.
If 14 is deleted from the data 12, 14, 15, 16, 17, 18, 19 and 20, then the median increases by
A) 1
B) 1.5
C) 2
D) 0.5
Answer:
D) 0.5
Question 28.
The mean of the first eight multiples of 3 is
A) 8
B) 13.5
C) 13
D) 27
Answer:
B) 13.5
Question 29.
If the mean of a, a + 3, a + 6, a + 9 and a + 12 is 10, then the value of ‘a’ is ……………. .
A) 1
B) 2
C) 3
D) 4
Answer:
D) 4
Question 30.
The class marks of a class interval is ………………. .
A) upper boundary + lower boundary
B) upper boundary – lower boundary
C) \(\frac{\text { upper boundary }+ \text { lower boundary }}{2}\)
D) \(\frac{\text { upper boundary }- \text { lower boundary }}{2}\)
Answer:
C) \(\frac{\text { upper boundary }+ \text { lower boundary }}{2}\)
Fill in the blanks :
1. If the mean of first n natural numbers is 16 then n = __________ .
Answer:
31
2. The mean of first n odd natural numbers is \(\frac{\mathrm{n}^2}{64}\) then n = __________ .
Answer:
64
3. 35 is removed from the data.30, 34, 35, 36, 37, 38, 39, 40 then the median increases by _________ .
Answer:
0.5
4. 3 median – 2 mean = __________ .
Answer:
mode
5. The sum of 12 observations is 600. Then their mean is __________ .
Answer:
50
6. The numbers 3, 5, 7 and 9 have their frequencies x – 2, x + 2, x – 3 and x + 3. If their mean is 6.5 then x = __________ .
Answer:
5
7. A set of numbers consists of three 4’s, five 5’s, six 6’s, eight 8’s, and seven 10’s. The mode of this set of numbers is _________ .
Answer:
8
8. For the data (2, 9, x + 6, 2x + 3, 5, 10, 5) mean is 7 then mode __________ .
Answer:
9
9. The A.M. of 20 fours, 40 fives, 30 sixes and 10 tens is __________ .
Answer:
5.6
10. The mean of a set of 20 observations is 19.3. The mean is reduced by 0.5 when a new observation is added to the set. Then the new observation is ___________ .
Answer:
8.8