JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Statistics

If the data

x_{1}, x_{2}, \dots ., x_{10}

is such that the mean of first four of these is 11 , the mean of the remaining six is 16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is:

(A) $22$
(B)2✓ Correct
(C)4
(D) $2$

Answer: (B)

Solution

The first four values sum to

4 \times 11 = 44

and the remaining six to

6 \times 16 = 96

, so the total is

140

and the mean is

\overset{x}{ˉ} = \frac{140}{10} = 14

. The variance is

σ^{2} = \frac{\sum x _{i}^{2}}{n} - \overset{x}{ˉ}^{2} = \frac{2000}{10} - 1 4^{2} = 200 - 196 = 4

, so the standard deviation is

σ = 4 = 2

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Statistics →

More JEE Main questions on Statistics

Let the mean and variance of 7 observations $2, 4, 10, x, 12, 14, y, x > y$ , be 8 and 16 respectively. Two numbers are chosen from ${1, 2, 3, x - 4, y, 5}$ one after another without replacement, then the probability, that the smaller number among the two chosen num …
JEE Main 2026View solution →
If the mean deviation about the median of the numbers $k, 2 k, 3 k, \dots, 1000 k$ is 500, then $k^{2}$ is equal to :
JEE Main 2026View solution →
Let the mean and variance of 8 numbers $- 10, - 7, - 1, x, y, 9, 2, 16$ be $\frac{7}{2}$ and $\frac{293}{4}$ , respectively. Then the mean of 4 numbers $x, y, x + y + 1, ∣ x - y ∣$ is:
JEE Main 2026View solution →
If the mean and the variance of the data

\begin{tabular}{|l|c|c|c|c|}
\hline Class & $4 - 8$ & $8 - 12$ & $12 - 16$ & $16 - 20$ \\
\hline Frequency & 3 & $λ$ & 4 & 7 \\
\hline
\end{tabular}

are $μ$ and 19 respectively, then the value of $λ + μ$ is
JEE Main 2026View solution →
The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observation $α$ in this data is replaced by $β$ , then the mean and variance become 10.1 and 1.99, respectively. Then $α + β$ equals.
JEE Main 2026View solution →
Let $X = {x \in N : 1 \leq x \leq 19}$ and for some $a, b \in R$ , $Y = {ax + b : x \in X}$ . If the mean and variance of the elements of Y are 30 and 750, respectively, th …
JEE Main 2026View solution →