State true or false:
Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows:

Then, the mean heartbeats per minute for these women is 75.4.

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An Intiative by Sri Chaitanya

True

False

answer is B.

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Detailed Solution

It is given a data,

Considering the assumed mean a = 75.5
Class size h = 68 – 65 = 3
By using the step-deviation method, the given data can be written as-
Question Image

From the table, we get

∑ f i = 30 ∑ f i u i = 4

Now, using the formula for mean-

M e a n (x ¯) = a + h × ∑ f i u i ∑ f i

Substituting the values, we get

⇒ M e a n (x ¯) = 75.5 + 3 × 430 ⇒ M e a n (x ¯) = 75.5 + 25 ⇒ M e a n (x ¯) = 75.5 + 0.4 ⇒ M e a n (x ¯) = 75.9

Hence, the mean heartbeats per minute for the given thirty women is 75.9.
Therefore, the given statement is false.
Hence the correct option is 2.

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