JEE Main · 2023 · 25 Jan 2023 · Shift 1 · Statistics

WhatsApp Email

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2. then their new variance is equal to :

(A)4.04
(B)4.08
(C)3.96✓ Correct
(D)3.92

Answer: (C)

Solution

From the mean change,

\frac{10 n + 4}{n} = 10.2

gives

n = 20

. The original variance

4 = \frac{\sum x _{i}^{2}}{20} - 100

gives

\sum x_{i}^{2} = 2080

, and replacing

8

12

changes this to

2080 - 64 + 144 = 2160

. The new variance is

\frac{2160}{20} - (10.2)^{2} = 108 - 104.04 = 3.96

JEE Main · 2023 · 25 Jan 2023 · 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 →