Question

Using the Classic Rock data in the Math 108 group on StatCrunch, create a histogram with the

Answer 1

The product of the frequency and PlayCount gives the number of songs

played from the information in the histogram.

Correct responses (rounded to the nearest whole integer)

1. 2%

2. 27 PlayCount per song

3. 68%

How does one analyze an histogram?

1. The given data from the histogram is presented in a tabular form as follows;

$\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}f&899&224&126&96&71&52&39&41&44&23&14&12&3&4&3\\x&10&20&30&40&50&60&70&80&90&100&110&120&130&140&150\end{array}\right]$

The percentages of song that where played over 100 times is given as follows;

∑f = 899+224+126+96+71+52+39+41+44+23+14+12+3+4+3 = 1651

Number of songs played over 100 times = 14 + 12 + 3 + 4 + 3 = 36

• $Percentage \ of \ songs \ played \ over \ 100 \ times = \mathbf{\dfrac{36}{1,651} \times 100} \approx \underline{2 \%}$

2. Mean of a frequency distribution is given as follows;

$Mean = \mathbf{\dfrac{\sum f\times x}{\sum f}}$

Where;

x = The PlayCount

From MS Excel, we have;

∑f·x = 44410

Which gives;

• $Mean = \dfrac{44410}{1651} \approx \underline{27}$

3. Number of songs played less than 20 times = 899 + 224 = 1,123

• $\mathbf{Percentage} \ of \ songs \ played \ less \ than \ 20 \ times = \dfrac{1,123}{1,651} \times 100 \approx \underline{ 68 \%}$

Learn more about percentages and histograms here:

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