Question

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

You must show all of your work to receive credit.

Answer 1

`Mean = 69`

`Mode = 66`

`Median = 69`

Explanation:

Given

The frequency table

Required

Determine the mean, median and mode

Calculating Mean

`Mean = (\sum fx)/(\sum f)`

Where

fx = product of frequency and inches

f = frequency

So;

`Mean = (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 = (1587)/(23)`

`Mean = 69`

Calculating Mode

`Mode = 66`

Because it highest frequency of 4

Calculating Median

`Median = (\sum f)/(2)th\ position`

`Median = (2 + 1 + 4 + 3 + 1 + 2 + 2 + 1 + 3 + 2 + 2)/(2)th\ position`

`Median = (23)/(2)th\ position`

`Median = 11.5th\ position`

Approximate

`Median = 12th\ position`

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

Inches ---- Frequency ---- CF

63 -------------2------------------2

65 -------------1------------------3

66 -------------4------------------7

67 -------------3------------------10

68 -------------1------------------11

69 -------------2------------------13

70 -------------2------------------15

71 -------------1------------------16

72 -------------3------------------19

74 -------------2------------------21

75 -------------2------------------23

From the above table

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

69 -------------2------------------13

because it has a CF greater than 12

Hence;

`Median = 69`