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Question 37

Number 37

Consider the following histogram!

Score Distribution Histogram

Frequency distribution of student scores.

The mode of the data shown in the histogram is ....

$61{,}0$

$61{,}5$

$62{,}0$

$62{,}6$

$63{,}5$

Explanation

To calculate the mode from histogram data, use the mode formula for grouped data.

Data Histogram

Score Distribution Histogram

Frequency distribution of student scores with the modal class indicated.

Determining the Modal Class

The modal class is the interval with the highest frequency, which is the interval $59.5 - 64.5$ with frequency $14$

Calculating Frequency Differences

Difference between modal class frequency and previous class frequency

d_1 = 14 - 9 = 5

Difference between modal class frequency and next class frequency

d_2 = 14 - 11 = 3

Determining Parameters

Lower boundary of modal class

T_b = 59.5

Class width

L = 64.5 - 59.5 = 5

Calculating the Mode

Using the mode formula for grouped data

M_o = T_b + \left(\frac{d_1}{d_1 + d_2}\right) \cdot L

= 59.5 + \left(\frac{5}{5 + 3}\right) \cdot 5

= 59.5 + \left(\frac{5}{8}\right) \cdot 5

= 59.5 + 3.125

= 62.625 \approx 62.6

Therefore, the mode of the data shown in the histogram is $62.6$

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Question 37Set 1

Exercises

Number 37

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