Question

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

Answer 1

Answer:

$Mean = 69$

$Mode = 66$

$Median = 69$

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)

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;

$Median = 69$