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Calculate the mode and mean of given data.

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Mode=6.67, Mean=14.08

Mode=67.7, Mean=14.88

Mode=30, Mean=91

Mode=26.8, Mean=42

answer is A.

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Detailed Solution

Given table is,
Question Image

Consider the table,
Question Image

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h

Where,

l

is the lower limit of the modal class.

f 1

is the frequency of the modal class.

f 2

is the frequency of the class succeeding the modal class.

f 0

is the frequency of the class preceding the modal class. h is the width of the class intervals.
The formula to find the mean is

x ¯ = ∑ f i x i ∑ f i

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h

The modal class of the grouped distribution is 0-10 having the highest frequency of 142.

l = 0 f 1 = 50 f 2 = 25 f 0 = 0 h = 10 − 0 ⇒ h = 10

Using the formula:

Mode = l + f 1 − f 0 2 f 1 − f 0 − f 2 × h ⇒ M o d e = 0 + 50 − 0 2 (50) − 0 − 25 × 10 ⇒ M o d e = 0 + 50 × 10 75 ⇒ M o d e = 6.67

The sum of frequency from the table is:

∑ f i = 50 + 25 + 10 + 8 + 5 ⇒ ∑ f i = 98

The sum of

f i x i

is:

∑ f i x i = 250 + 375 + 250 + 280 + 225 = 1380

Using the formula of mean we have:

x ¯ = ∑ f i x i ∑ f i ⇒ x ¯ = 138098 ⇒ x ¯ = 14.08

A maximum number of frequencies will have the variable 6.67, while on average the variable of a frequency can be 14.08.
Hence, option 1 is correct.

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