Question

the mean of a certain group of observations is 150.find the new mean, if the value of each observations is: decreased by 26%​

Answer 1

Required Answer:

GiveN:

• The Mean of a certain data is 150.
• Each observations in the data is decreased by 26%.

To FinD:

• New mean of the data?

Step-wise-Step Explanation:

When all the observations in a certain data suffers from any kind of change like above, the new mean will also vary in the same way.

That means, the mean will decrease by 26%.

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Why so?

Mean = Sum of all obs. / No. of obs.

Sum of all obs. = m1 + m2 + m3 .........m_n

No. of obs. = n

Mean = m1 + m2 +.....m_n / n

After decreasing by 26%

Sum of all obs. = 74 m1/100 + 74 m2/100.....74 m_n/100

No. of obs. = n

New mean = 74 m1/100 +.....74 m_n/100 / n

⇒ New mean = 74/100{ m1 +......m_n} / n

⇒ New mean = 74/100 × Original mean⬆️

Hence, Mean also decreases by 26%.

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We have,

• Original mean = 150
• Percentage decrease = 26%

New mean:

= Original mean - 26% of Original mean

= 150 - 26/100 × 150

= 150 - 39

= 111

Hence,

The required new mean is:

$\huge{ \boxed{ \sf{ \red{111}}}}$

Answer 2

Explanation :-

When all the observations in a certain data suffers from any kind of change like above, the new mean will also vary in the same way.

That means, the mean will decrease by 26%.

Why so?

Mean = Sum of all obs. / No. of obs.

Sum of all obs. = m1 + m2 + m3 .........m_n

No. of obs. = n

Mean = m1 + m2 +.....m_n / n

After decreasing by 26%

Sum of all obs. = 74 m1/100 + 74 m2/100.....74 m_n/100

No. of obs. = n

New mean = 74 m1/100 +.....74 m_n/100 / n

⇒ New mean = 74/100{ m1 +......m_n} / n

⇒ New mean = 74/100 × Original mean

Hence,

Mean also decreases by 26%.

We have,

Original mean = 150

Percentage decrease = 26%

New mean:

= Original mean - 26% of Original mean

= 150 - 26/100 × 150

= 150 - 39

= 111

Hence,

• The required new mean is : 111