Statistics PYQs Set 1 (PDF)

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Mere Teacher · Previous Year Questions

JEE Main Mathematics · Statistics · Set 1 (Q1-30)

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1.
If the standard deviation of the numbers $- 1, 0$ , $1, k$ is $5$ where $k > 0$ , then $k$ is equal to
1. (1) $4 \frac{5}{3}$
2. (2) $2 \frac{10}{3}$
3. (3) $6$
4. (4) $26$
2.
If 10 is the mean of the data $2, 3, 5, 18, 17, 15, 13, x, 9$ and 7 , then the mean deviation of this data about its mean is
1. (1) $4.7$
2. (2) $4.8$
3. (3) $4.9$
4. (4) $5.0$
3.
The coefficient of variation of $9, 3, 11, 5, 7$ , is
1. (1) $\frac{100 2}{7}$
2. (2) $\frac{200 2}{3}$
3. (3) $\frac{200 2}{7}$
4. (4) $\frac{100 2}{3}$
4.
The mean deviation from the mean for the observations $1, 3, 5, 7, 11, 13, 17, 19, 23$ is
1. (1) $6$
2. (2) $11 \frac{4}{9}$
3. (3) $11$
4. (4) $6 \frac{2}{9}$
5.
For the set $A = (x_{1}, x_{2}, x_{3}, x_{4}, x_{5})$ the variance is 4 and the mean is 2 . For the set $B = (y_{1}, y_{2}, y_{3}, y_{4}, y_{5})$ the variance is 5 and the mean is 4 . Then, the variance of $A \cup B$ is
1. (1) $6$
2. (2) $6.5$
3. (3) $5.5$
4. (4) $5$
6.
The mean deviation from the mean of the discrete data $1, 3, 4, 7, 11, 18, 29, 47, 78$ is
1. (1) $22$
2. (2) $24$
3. (3) $\frac{176}{9}$
4. (4) $\frac{182}{9}$
7.
The standard deviation of first 10 multiples of 4 is
1. (1) $7$
2. (2) $8$
3. (3) $11.5$
4. (4) $14$
8.
If 10 is the mean deviation of ' $n$ ' observations $x_{1}, x_{2}$ , $x_{3}, \dots, x_{n}$ then the mean deviation of the observations $\frac{2 x _{1} + 5}{3}, \frac{2 x _{2} + 5}{3}, \frac{2 x _{3} + 5}{3}, \dots ., \frac{2 x _{n} + 5}{3}$ is
1. (1) $\frac{25}{3}$
2. (2) $\frac{40}{9}$
3. (3) $\frac{20}{3}$
4. (4) $15$
9.
The arithmetic mean of the observations $10, 8, 5, a, b$ is 6 and their variance is 6.8, then $ab$ is equal to
1. (1) $6$
2. (2) $4$
3. (3) $3$
4. (4) $12$
10.
If the variance of the frequency distribution
$x$
$c$
$2 c$
$3 c$
$4 c$
$5 c$
$6 c$
$f$
2
1
1
1
1
1
is 160 , then the value of $c \in N$ is
1. (1) $7$
2. (2) $8$
3. (3) $5$
4. (4) $6$
11.
If the standard deviation of the numbers $2, 3, 2 x$ and 11 is 3.5. Find the possible values of $x$ .
1. (1) $2, \frac{7}{2}$
2. (2) $3, \frac{5}{3}$
3. (3) $2, \frac{5}{2}$
4. (4) $3, \frac{7}{3}$
12.
Let the mean and standard deviation of marks of class A of 100 students be respectively 40 $α (> 0)$ , and the mean and standard deviation of marks of class B of n students be respectively 55 and 30- $α$ . If the mean and variance of the marks of the combined class of 100 + n students are respectively 50 and 350, then the sum of variance of classes A and B is
1. (1) $500$
2. (2) $650$
3. (3) $450$
4. (4) $900$
13.
The mean and standard deviation of 100 observations are 40 and 5.1, respectively. By mistake one observation is taken as 50 instead of 40. If the correct mean and the correct standard deviation are $μ$ and $σ$ respectively, then $10 (μ + σ)$ is equal to
1. (1) $447$
2. (2) $445$
3. (3) $449$
4. (4) $451$
14.
For the following frequency distribution, the variance is approximately equal to
Class Interval
$0 - 5$
$5 - 10$
$10 - 15$
$15 - 20$
$20 - 25$
Frequency
4
1
10
3
2
1. (1) $33.1$
2. (2) $30.55$
3. (3) $34.75$
4. (4) $37.50$
15.
Let $a_{1}, a_{2}, \dots a_{10}$ be 10 observations such that $\sum_{k = 1}^{10} a_{k} = 50$ and $\sum_{\forall k < j} a_{k} \cdot a_{j} = 1100$ . Then the standard deviation of $a_{1}, a_{2}, \dots, a_{10}$ is equal to :
1. (1) $5$
2. (2) $5$
3. (3) $10$
4. (4) $115$
16.
The mean deviation about the mean for the following data is
Class Interval
$0 - 4$
$4 - 8$
$8 - 12$
$12 - 16$
Frequency
4
3
2
1
1. (1) $6$
2. (2) $3.6$
3. (3) $3.2$
4. (4) $10$
17.
If the coefficient of variation and variance of a frequency distribution are 7.2 and 3.24 respectively, then its mean is
1. (1) $45$
2. (2) $25$
3. (3) $20$
4. (4) $16$
18.
If the mean and the standard deviation of the data 3, 5, 7, $a, b$ are 5 and 2 respectively, then $a$ and $b$ are the roots of the equations:
1. (1) $x^{2} - 20 x + 18 = 0$
2. (2) $2 x^{2} - 20 x + 19 = 0$
3. (3) $x^{2} - 10 x + 18 = 0$
4. (4) $x^{2} - 10 x + 19 = 0$
19.
There rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If $μ$ and $σ^{2}$ represent mean and variance of X, respectively, then 10 $(μ^{2} + σ^{2})$ is equal to
1. (1) $20$
2. (2) $250$
3. (3) $25$
4. (4) $30$
20.
In a data, if the number $i$ is repeated $i$ times for $i = 1, 2$ , ..... $n$ , then the mean of the data is
1. (1) $\frac{2 n + 1}{6}$
2. (2) $\frac{2 n + 1}{4}$
3. (3) $\frac{2 n + 1}{3}$
4. (4) $\frac{2 n + 1}{2}$
21.
Let the mean and the variance of 6 observation $a, b, 68, 44, 48, 60$ be 55 and 194 , respectively if $a > b$ , then $a + 3 b$ is
1. (1) $200$
2. (2) $190$
3. (3) $180$
4. (4) $210$
22.
$The mean deviation about the mean of the following data is nearly$
$Size (x)$ $1$ $3$ $5$ $7$ $9$ $11$ $13$ $15$
$Frequency (f)$ $3$ $3$ $4$ $14$ $7$ $4$ $3$ $4$
1. (1) $3.45$
2. (2) $3.25$
3. (3) $2.75$
4. (4) $2.95$
23.
Let the Mean and Variance of five observations $x_{1} = 1, x_{2} = 3, x_{3} = a, x_{4} = 7$ and $x_{5} = b, a > b$ , be 5 and 10 respectively. Then the Variance of the observations $n + x_{n}, n = 1, 2, \dots, 5$ is
1. (1) $17$
2. (2) $16$
3. (3) $16.4$
4. (4) $17.4$
24.
If $α \neq = 0$ and the mean deviation of the observations ${k α}$ , for $k = 1, 2, \dots \dots ., 50$ about its median is 50, then $| α | =$
1. (1) $4$
2. (2) $3$
3. (3) $2$
4. (4) $5$
25.
There are $n$ observations and all of them are negative numbers. The ascending order of these observations is $x_{1}, x_{2}, \dots, x_{n}$ . If the signs of the first term and last term in that order are changed, then the range of the data is
1. (1) $∣ x_{1} ∣ - ∣ x_{n} ∣$
2. (2) $(x_{n} - x_{1})$
3. (3) $∣ x_{1} ∣ - x_{2}$
4. (4) $∣ x_{1} ∣ - ∣ x_{2} ∣$
26.
If for some positive $x \in R$ , the frequency distribution of the marks obtained by 20 students in a certain test, is as follows:
Marks
2
3
5
7
Frequency
$(x + 1)^{2}$
$2 x - 5$
$x^{2} - 3 x$
$x$
Then the mean of the marks is
1. (1) $3.2$
2. (2) $3.0$
3. (3) $2.8$
4. (4) $2.5$
27.
$The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacheris appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years)of the newly appointedteacher is_____$
28.
$The variance of the numbers 8, 21, 34, 47, \dots, 320 is$
29.
$If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x ∙ y is equal to \dots$
30.
$From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable X denote the number of defective items in the sample. If the variance of X is σ^{2}, then 96 σ^{2} is equal to______$