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Mrac [35]
3 years ago
6

Using the frequency table given, find the mean, median, and mode.

Mathematics
1 answer:
aalyn [17]3 years ago
7 0

Answer:

Mean = 69

Mode = 66

<em />Median = 69<em />

<em />

Step-by-step explanation:

Given

The frequency table

Required

Determine the mean, median and mode

Calculating Mean

Mean = \frac{\sum fx}{\sum f}

Where

fx = product of frequency and inches

f = frequency

So;

Mean = \frac{63 * 2 + 65 * 1 + 66 * 4 + 67 * 3 + 68 * 1 + 69 * 2 + 70 * 2 + 71 * 1 + 72 * 3 + 74 * 2 + 75 * 2}{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}

Mean = \frac{1587}{23}

Mean = 69

Calculating Mode

Mode = 66

Because it highest frequency of 4

Calculating Median

Median = \frac{\sum f}{2}th\ position

Median = \frac{2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2}{2}th\ position

Median = \frac{23}{2}th\ position

Median = 11.5th\ position

Approximate

Median = 12th\ position

At this point we, need to get the cumulative frequency (CF)

<em>Inches ---- Frequency ---- CF</em>

<em>63 -------------2------------------2</em>

<em>65 -------------1------------------3</em>

<em>66 -------------4------------------7</em>

<em>67 -------------3------------------10</em>

<em>68 -------------1------------------11</em>

<em>69 -------------2------------------13</em>

<em>70 -------------2------------------15</em>

<em>71 -------------1------------------16</em>

<em>72 -------------3------------------19</em>

<em>74 -------------2------------------21</em>

<em>75 -------------2------------------23</em>

From the above table

Since the median fall in the 12th position, then we consider the following data

<em>69 -------------2------------------13</em>

<em>because it has a CF greater than 12</em>

<em />

<em>Hence;</em>

<em />Median = 69<em />

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