Calculate the mean of the frequency distribution shown in the table and histogram.

Question

ScanSolve AI Tutor · Accepted Answer

The image displays a frequency distribution table and a histogram. Since no specific question was asked, I will calculate the mean of the distribution, which is a common task for such data.

Identify the class centers ( $x$ ) and frequencies ( $f$ ) from the table.

The class centers are already provided in the table.

Class limits	Frequency ( $f$ )	Class center ( $x$ )
$40 - 49$	13	44.5
$50 - 59$	9	54.5
$60 - 69$	6	64.5
$70 - 79$	8	74.5
$80 - 89$	8	84.5
$90 - 99$	1	94.5

Calculate the product of frequency and class center ( $f \cdot x$ ) for each class.
For $40 - 49$ : $13 \times 44.5 = 578.5$
For $50 - 59$ : $9 \times 54.5 = 490.5$
For $60 - 69$ : $6 \times 64.5 = 387.0$
For $70 - 79$ : $8 \times 74.5 = 596.0$
For $80 - 89$ : $8 \times 84.5 = 676.0$
For $90 - 99$ : $1 \times 94.5 = 94.5$
Calculate the sum of frequencies ( $\sum f$ ) and the sum of the products ( $\sum (f \cdot x)$ ).
$\sum f = 13 + 9 + 6 + 8 + 8 + 1 = 45$ $\sum (f \cdot x) = 578.5 + 490.5 + 387.0 + 596.0 + 676.0 + 94.5 = 2822.5$
Calculate the mean ( $\bar{x}$ ) using the formula $\bar{x} = \frac{\sum (f \cdot x)}{\sum f}$ .
$\bar{x} = \frac{2822.5}{45}$ $\bar{x} \approx 62.7222...$
Rounding to two decimal places:
$\bar{x} \approx 62.72$
The mean of the distribution is $\text{62.72}$ .

Calculate the mean of the frequency distribution shown in the table and histogram.

Answer

Step-by-step solution

Identify the class centers ( $x$ ) and frequencies ( $f$ ) from the table.

Calculate the product of frequency and class center ( $f \cdot x$ ) for each class.

Calculate the sum of frequencies ( $\sum f$ ) and the sum of the products ( $\sum (f \cdot x)$ ).

Calculate the mean ( $\bar{x}$ ) using the formula $\bar{x} = \frac{\sum (f \cdot x)}{\sum f}$ .

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More Mathematics Questions

Calculate the mean of the frequency distribution shown in the table and histogram.

Answer

Step-by-step solution

Identify the class centers (xxx) and frequencies (fff) from the table.

Calculate the product of frequency and class center (f⋅xf \cdot xf⋅x) for each class.

Calculate the sum of frequencies (∑f\sum f∑f) and the sum of the products (∑(f⋅x)\sum (f \cdot x)∑(f⋅x)).

Calculate the mean (xˉ\bar{x}xˉ) using the formula xˉ=∑(f⋅x)∑f\bar{x} = \frac{\sum (f \cdot x)}{\sum f}xˉ=∑f∑(f⋅x)​.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Identify the class centers ( $x$ ) and frequencies ( $f$ ) from the table.

Calculate the product of frequency and class center ( $f \cdot x$ ) for each class.

Calculate the sum of frequencies ( $\sum f$ ) and the sum of the products ( $\sum (f \cdot x)$ ).

Calculate the mean ( $\bar{x}$ ) using the formula $\bar{x} = \frac{\sum (f \cdot x)}{\sum f}$ .