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Model Paper 5 — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsModel Paper 51 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
$\bar{x}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_i}{n}$
$=\frac{4+7+8+9+10+12+13+17}{8}=10$
xi$| x i - x |$
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
$\bar{x}=\frac{\text { Sum of terms }}{\text { Number of terms }}=\frac{\sum x_{i}}{n}$
$=\frac{38+70+48+40+42+55}{+63+46+54+44}=50$
$\therefore$ Mean deviation about mean
$=\frac{\Sigma\left|x_{i}-\bar{x}\right|}{n}$
$=\frac{84}{10}=8.4$
Hence, Assertion is true and Reason is false.

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