Assertion -If mean of 7 observation is 10 mean of set of 3 observation is 5 - then mean of combined set is 8-5- Reason- If x-1-x-2- be the mean of n1 - n2 observations respectively- then combined mean is n1x-1-n2x-2-n1-n2

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Probability

Assertion :If...

Question

Assertion :If mean of $7$ observation is $10$ & mean of set of $3$ observation is $5$ , then mean of combined set is $8.5$ . Reason: If $_{1} &_{2}$ be the mean of $n_{1} & n_{2}$ observations respectively, then combined mean is $\frac{n_{1}_{1} + n_{2}_{2}}{n_{1} + n_{2}}$

Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Assertion is true Reason is false.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Assertion is false Reason is true.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.
$∵ n_{1} = 7, {¯ x}_{1} = 10 a n d n_{2} = 3, {¯ x}_{2} = 5$
$∴$ Combined mean $= \frac{n_{1} {¯ x}_{1} + n_{2} {¯ x}_{2}}{n_{1} + n_{2}}$
$= \frac{7 \times 10 + 3 \times 5}{7 + 3} = 8.5$

Suggest Corrections

Similar questions

Q. Assertion: The mean of 15 numbers is 25. If 6 is subtracted from each number, the mean of new numbers is 19.
Reason: Mode = 3(median) − 2(mean).
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. Assertion (A)
If the median and mode of a frequency distribution are 150 and 154 respectively, then its mean is 148.
Reason (R)
Mean, median and mode of a frequency distribution are related as:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is a not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion : The median of the following observation 0, 1, 2, 3, x, x+2, 8, 9, 11, 12 which arranged in ascending order is 63, then the value of x is 62.
Reason : Median of n even observations is

\frac{{(\frac{n}{2})}^{t h} t e r m + {(\frac{n}{2} + 1)}^{t h} t e r m}{2}

Which of the following is correct.

Q. Assertion: Median of 51, 70, 65, 82, 60, 68, 62, 95, 55, 64, 58, 75, 80, 85, 90 is 68.
Reason: When n observations are arranged in an ascending order and n is odd, then

median = value of \frac{1}{2} (n + 1)

th observation.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Assertion: If $a \neq b$ , then $(a, b) \neq (b, a)$ .
Reason: $(4, - 3)$ lies in Quadrant $I V$
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Join BYJU'S Learning Program

Assertion :If mean of 7 observation is 10 & mean of set of 3 observation is 5 , then mean of combined set is 8.5. Reason: If ¯x1&¯x2 be the mean of n1 & n2 observations respectively, then combined mean is n1¯x1+n2¯x2n1+n2

The correct option is A Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.∵n1=7,¯x1=10 and n2=3,¯x2=5∴ Combined mean =n1¯x1+n2¯x2n1+n2=7×10+3×57+3=8.5

Assertion :If mean of $7$ observation is $10$ & mean of set of $3$ observation is $5$ , then mean of combined set is $8.5$ . Reason: If $_{1} &_{2}$ be the mean of $n_{1} & n_{2}$ observations respectively, then combined mean is $\frac{n_{1}_{1} + n_{2}_{2}}{n_{1} + n_{2}}$