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State whether the given statement is true or false.

If the table represents the weight of 12 players.

Then the mean weight of players is 50 kg, the median weight is 51 kg and the mode weight of players is calculated to be 48 kg by using the empirical formula.

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True

False

answer is A.

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Detailed Solution

Given data,
Question Image

Calculating the cumulative frequency of the given data;
Question Image

N=12 (even no. of terms).
Now, we will calculate median,

= 12 N 2 t h observation + N 2 + 1 t h observation

Substituting the values,
Question Image

Thus, the median is 50 kg.
Let’s calculate mean by using the formula and substituting the values,

= ∑ f 1 × x 1 ∑ f 1 = 61212 = 51

Thus, the mean is 51 kg.
The mode of the data by using the empirical formula is,
= 3(Median) - 2(Mean)
Substituting the values in the formula,

= 3 Median − 2 Mean = 350 − 251 = 150 − 102 = 48

Thus, the mode is 48 kg.
Hence, option 1 is correct, and the given statement is true.

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