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Model Paper 1 — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSModel Paper 11 Mark
MCQ
Assertion (A): The mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17 is 3.
Reason (R): The mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44 is 8.5.
  • A
    Both A and R are true and R is the correct explanation of A.
  • B
    Both A and R are true but R is not the correct explanation of A.
  • C
    A is true but R is false.
  • D
    A is false but R is true.
✓

Answer

(c) A is true but R is false. 
Explanation: Assertion: Mean of the given series 
$\begin{array}{l}\overline{\bar{x}}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_i}{n} \\ 
=\frac{4+7+8+9+10+12+13+17}{8}=10\end{array}$
xi$| x i -\bar{x}|$
4$|4-10|=6$
7$|7-10|=3$
8$|8-10|=2$
9$|9-10|=1$
10$|10-10|=0$
12$|12-10|=2$
13$|13-10|=3$
17$|17-10|=7$
$\sum x_i=80$$\sum\left|x_i-\bar{x}\right|=24$
$\therefore$ Mean deviation about mean
$=\frac{\Sigma\left|x_i-\bar{x}\right|}{n}=\frac{24}{8}=3$
Reason Mean of the given series 
$\begin{array}{l}\bar{x}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_i}{n} \\ =\frac{38+70+48+40+42+55}{+63+46+54+44}=50\end{array}$
$\therefore$ Mean deviation about mean
$\begin{array}{l}=\frac{\Sigma\left|x_i-\bar{x}\right|}{n} \\ 
=\frac{84}{10}=8.4\end{array}$
Hence, Assertion is true and Reason is false.

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